Table of Gaussian integer factorizations

Nomenclature

Gaussian integers may be categorized as units, Gaussian primes and composites. This is a list of Gaussian Integers x+i*y in the first quadrant followed either by an equal sign and an explicit factorization or followed by a label (p) for primes. The factorizations take the form of an optional unit multiplied by integer powers of Gaussian primes. They are usually not unique in the sense that the unit could be absorbed into any other factor with exponent equal to one.

The entries are sorted according to increasing norm x²+y² as listed in the OEIS^[1]. Primes occur only for norms also tabulated in the OEIS^[2], and are tabulated in A103431^[3] and A103432^[4].

Factorizations

norm 2

1+i (p)

norm 4

2 = -i*(1+i)²

norm 5

1+2*i (p)
2+i (p)

norm 8

2+2*i = -i*(1+i)³

norm 9

3 (p)

norm 10

1+3*i = (1+i)*(2+i)
3+i = (1+i)*(2-i)

norm 13

2+3*i (p)
3+2*i (p)

norm 16

4 = -(1+i)⁴

norm 17

1+4*i (p)
4+i (p)

norm 18

3+3*i = (1+i)*3

norm 20

2+4*i = (1+i)²*(2-i)
4+2*i = -i*(1+i)²*(2+i)

norm 25

3+4*i = (2+i)²
4+3*i = i*(2-i)²
5 = (2+i)*(2-i)

norm 26

1+5*i = (1+i)*(3+2*i)
5+i = (1+i)*(3-2*i)

norm 29

2+5*i (p)
5+2*i (p)

norm 32

4+4*i = -(1+i)⁵

norm 34

3+5*i = (1+i)*(4+i)
5+3*i = (1+i)*(4-i)

norm 36

6 = -i*(1+i)²*3

norm 37

1+6*i (p)
6+i (p)

norm 40

2+6*i = -i*(1+i)³*(2+i)
6+2*i = -i*(1+i)³*(2-i)

norm 41

4+5*i (p)
5+4*i (p)

norm 45

3+6*i = i*(2-i)*3
6+3*i = (2+i)*3

norm 49

7 (p)

norm 50

1+7*i = i*(1+i)*(2-i)²
5+5*i = (1+i)*(2+i)*(2-i)
7+i = -i*(1+i)*(2+i)²

norm 52

4+6*i = (1+i)²*(3-2*i)
6+4*i = -i*(1+i)²*(3+2*i)

norm 53

2+7*i (p)
7+2*i (p)

norm 58

3+7*i = (1+i)*(5+2*i)
7+3*i = (1+i)*(5-2*i)

norm 61

5+6*i (p)
6+5*i (p)

norm 64

8 = i*(1+i)⁶

norm 65

1+8*i = i*(2+i)*(3-2*i)
4+7*i = (2+i)*(3+2*i)
7+4*i = i*(2-i)*(3-2*i)
8+i = (2-i)*(3+2*i)

norm 68

2+8*i = (1+i)²*(4-i)
8+2*i = -i*(1+i)²*(4+i)

norm 72

6+6*i = -i*(1+i)³*3

norm 73

3+8*i (p)
8+3*i (p)

norm 74

5+7*i = (1+i)*(6+i)
7+5*i = (1+i)*(6-i)

norm 80

4+8*i = -i*(1+i)⁴*(2-i)
8+4*i = -(1+i)⁴*(2+i)

norm 81

9 = 3²

norm 82

1+9*i = (1+i)*(5+4*i)
9+i = (1+i)*(5-4*i)

norm 85

2+9*i = i*(2-i)*(4+i)
6+7*i = i*(2-i)*(4-i)
7+6*i = (2+i)*(4+i)
9+2*i = (2+i)*(4-i)

norm 89

5+8*i (p)
8+5*i (p)

norm 90

3+9*i = (1+i)*(2+i)*3
9+3*i = (1+i)*(2-i)*3

norm 97

4+9*i (p)
9+4*i (p)

norm 98

7+7*i = (1+i)*7

norm 100

6+8*i = -i*(1+i)²*(2+i)²
8+6*i = (1+i)²*(2-i)²
10 = -i*(1+i)²*(2+i)*(2-i)

norm 101

1+10*i (p)
10+i (p)

norm 104

2+10*i = -i*(1+i)³*(3+2*i)
10+2*i = -i*(1+i)³*(3-2*i)

norm 106

5+9*i = (1+i)*(7+2*i)
9+5*i = (1+i)*(7-2*i)

norm 109

3+10*i (p)
10+3*i (p)

norm 113

7+8*i (p)
8+7*i (p)

norm 116

4+10*i = (1+i)²*(5-2*i)
10+4*i = -i*(1+i)²*(5+2*i)

norm 117

6+9*i = i*3*(3-2*i)
9+6*i = 3*(3+2*i)

norm 121

11 (p)

norm 122

1+11*i = (1+i)*(6+5*i)
11+i = (1+i)*(6-5*i)

norm 125

2+11*i = (2+i)³
5+10*i = i*(2+i)*(2-i)²
10+5*i = (2+i)²*(2-i)
11+2*i = i*(2-i)³

norm 128

8+8*i = i*(1+i)⁷

norm 130

3+11*i = i*(1+i)*(2-i)*(3-2*i)
7+9*i = (1+i)*(2-i)*(3+2*i)
9+7*i = (1+i)*(2+i)*(3-2*i)
11+3*i = -i*(1+i)*(2+i)*(3+2*i)

norm 136

6+10*i = -i*(1+i)³*(4+i)
10+6*i = -i*(1+i)³*(4-i)

norm 137

4+11*i (p)
11+4*i (p)

norm 144

12 = -(1+i)⁴*3

norm 145

1+12*i = i*(2-i)*(5+2*i)
8+9*i = (2+i)*(5+2*i)
9+8*i = i*(2-i)*(5-2*i)
12+i = (2+i)*(5-2*i)

norm 146

5+11*i = (1+i)*(8+3*i)
11+5*i = (1+i)*(8-3*i)

norm 148

2+12*i = (1+i)²*(6-i)
12+2*i = -i*(1+i)²*(6+i)

norm 149

7+10*i (p)
10+7*i (p)

norm 153

3+12*i = i*3*(4-i)
12+3*i = 3*(4+i)

norm 157

6+11*i (p)
11+6*i (p)

norm 160

4+12*i = -(1+i)⁵*(2+i)
12+4*i = -(1+i)⁵*(2-i)

norm 162

9+9*i = (1+i)*3²

norm 164

8+10*i = (1+i)²*(5-4*i)
10+8*i = -i*(1+i)²*(5+4*i)

norm 169

5+12*i = (3+2*i)²
12+5*i = i*(3-2*i)²
13 = (3+2*i)*(3-2*i)

norm 170

1+13*i = (1+i)*(2+i)*(4+i)
7+11*i = (1+i)*(2+i)*(4-i)
11+7*i = (1+i)*(2-i)*(4+i)
13+i = (1+i)*(2-i)*(4-i)

norm 173

2+13*i (p)
13+2*i (p)

norm 178

3+13*i = (1+i)*(8+5*i)
13+3*i = (1+i)*(8-5*i)

norm 180

6+12*i = (1+i)²*(2-i)*3
12+6*i = -i*(1+i)²*(2+i)*3

norm 181

9+10*i (p)
10+9*i (p)

norm 185

4+13*i = i*(2-i)*(6+i)
8+11*i = i*(2-i)*(6-i)
11+8*i = (2+i)*(6+i)
13+4*i = (2+i)*(6-i)

norm 193

7+12*i (p)
12+7*i (p)

norm 194

5+13*i = (1+i)*(9+4*i)
13+5*i = (1+i)*(9-4*i)

norm 196

14 = -i*(1+i)²*7

norm 197

1+14*i (p)
14+i (p)

norm 200

2+14*i = (1+i)³*(2-i)²
10+10*i = -i*(1+i)³*(2+i)*(2-i)
14+2*i = -(1+i)³*(2+i)²

norm 202

9+11*i = (1+i)*(10+i)
11+9*i = (1+i)*(10-i)

norm 205

3+14*i = i*(2+i)*(5-4*i)
6+13*i = (2+i)*(5+4*i)
13+6*i = i*(2-i)*(5-4*i)
14+3*i = (2-i)*(5+4*i)

norm 208

8+12*i = -i*(1+i)⁴*(3-2*i)
12+8*i = -(1+i)⁴*(3+2*i)

norm 212

4+14*i = (1+i)²*(7-2*i)
14+4*i = -i*(1+i)²*(7+2*i)

norm 218

7+13*i = (1+i)*(10+3*i)
13+7*i = (1+i)*(10-3*i)

norm 221

5+14*i = i*(3-2*i)*(4+i)
10+11*i = (3+2*i)*(4+i)
11+10*i = i*(3-2*i)*(4-i)
14+5*i = (3+2*i)*(4-i)

norm 225

9+12*i = (2+i)²*3
12+9*i = i*(2-i)²*3
15 = (2+i)*(2-i)*3

norm 226

1+15*i = (1+i)*(8+7*i)
15+i = (1+i)*(8-7*i)

norm 229

2+15*i (p)
15+2*i (p)

norm 232

6+14*i = -i*(1+i)³*(5+2*i)
14+6*i = -i*(1+i)³*(5-2*i)

norm 233

8+13*i (p)
13+8*i (p)

norm 234

3+15*i = (1+i)*3*(3+2*i)
15+3*i = (1+i)*3*(3-2*i)

norm 241

4+15*i (p)
15+4*i (p)

norm 242

11+11*i = (1+i)*11

norm 244

10+12*i = (1+i)²*(6-5*i)
12+10*i = -i*(1+i)²*(6+5*i)

norm 245

7+14*i = i*(2-i)*7
14+7*i = (2+i)*7

norm 250

5+15*i = (1+i)*(2+i)²*(2-i)
9+13*i = i*(1+i)*(2-i)³
13+9*i = -i*(1+i)*(2+i)³
15+5*i = (1+i)*(2+i)*(2-i)²

norm 256

16 = (1+i)⁸

norm 257

1+16*i (p)
16+i (p)

norm 260

2+16*i = (1+i)²*(2+i)*(3-2*i)
8+14*i = -i*(1+i)²*(2+i)*(3+2*i)
14+8*i = (1+i)²*(2-i)*(3-2*i)
16+2*i = -i*(1+i)²*(2-i)*(3+2*i)

norm 261

6+15*i = i*3*(5-2*i)
15+6*i = 3*(5+2*i)

norm 265

3+16*i = i*(2-i)*(7+2*i)
11+12*i = i*(2-i)*(7-2*i)
12+11*i = (2+i)*(7+2*i)
16+3*i = (2+i)*(7-2*i)

norm 269

10+13*i (p)
13+10*i (p)

norm 272

4+16*i = -i*(1+i)⁴*(4-i)
16+4*i = -(1+i)⁴*(4+i)

norm 274

7+15*i = (1+i)*(11+4*i)
15+7*i = (1+i)*(11-4*i)

norm 277

9+14*i (p)
14+9*i (p)

norm 281

5+16*i (p)
16+5*i (p)

norm 288

12+12*i = -(1+i)⁵*3

norm 289

8+15*i = i*(4-i)²
15+8*i = (4+i)²
17 = (4+i)*(4-i)

norm 290

1+17*i = i*(1+i)*(2-i)*(5-2*i)
11+13*i = (1+i)*(2+i)*(5-2*i)
13+11*i = (1+i)*(2-i)*(5+2*i)
17+i = -i*(1+i)*(2+i)*(5+2*i)

norm 292

6+16*i = (1+i)²*(8-3*i)
16+6*i = -i*(1+i)²*(8+3*i)

norm 293

2+17*i (p)
17+2*i (p)

norm 296

10+14*i = -i*(1+i)³*(6+i)
14+10*i = -i*(1+i)³*(6-i)

norm 298

3+17*i = (1+i)*(10+7*i)
17+3*i = (1+i)*(10-7*i)

norm 305

4+17*i = i*(2+i)*(6-5*i)
7+16*i = (2+i)*(6+5*i)
16+7*i = i*(2-i)*(6-5*i)
17+4*i = (2-i)*(6+5*i)

norm 306

9+15*i = (1+i)*3*(4+i)
15+9*i = (1+i)*3*(4-i)

norm 313

12+13*i (p)
13+12*i (p)

norm 314

5+17*i = (1+i)*(11+6*i)
17+5*i = (1+i)*(11-6*i)

norm 317

11+14*i (p)
14+11*i (p)

norm 320

8+16*i = -(1+i)⁶*(2-i)
16+8*i = i*(1+i)⁶*(2+i)

norm 324

18 = -i*(1+i)²*3²

norm 325

1+18*i = (2+i)²*(3+2*i)
6+17*i = i*(2-i)²*(3+2*i)
10+15*i = i*(2+i)*(2-i)*(3-2*i)
15+10*i = (2+i)*(2-i)*(3+2*i)
17+6*i = (2+i)²*(3-2*i)
18+i = i*(2-i)²*(3-2*i)

norm 328

2+18*i = -i*(1+i)³*(5+4*i)
18+2*i = -i*(1+i)³*(5-4*i)

norm 333

3+18*i = i*3*(6-i)
18+3*i = 3*(6+i)

norm 337

9+16*i (p)
16+9*i (p)

norm 338

7+17*i = i*(1+i)*(3-2*i)²
13+13*i = (1+i)*(3+2*i)*(3-2*i)
17+7*i = -i*(1+i)*(3+2*i)²

norm 340

4+18*i = (1+i)²*(2-i)*(4+i)
12+14*i = (1+i)²*(2-i)*(4-i)
14+12*i = -i*(1+i)²*(2+i)*(4+i)
18+4*i = -i*(1+i)²*(2+i)*(4-i)

norm 346

11+15*i = (1+i)*(13+2*i)
15+11*i = (1+i)*(13-2*i)

norm 349

5+18*i (p)
18+5*i (p)

norm 353

8+17*i (p)
17+8*i (p)

norm 356

10+16*i = (1+i)²*(8-5*i)
16+10*i = -i*(1+i)²*(8+5*i)

norm 360

6+18*i = -i*(1+i)³*(2+i)*3
18+6*i = -i*(1+i)³*(2-i)*3

norm 361

19 (p)

norm 362

1+19*i = (1+i)*(10+9*i)
19+i = (1+i)*(10-9*i)

norm 365

2+19*i = i*(2-i)*(8+3*i)
13+14*i = (2+i)*(8+3*i)
14+13*i = i*(2-i)*(8-3*i)
19+2*i = (2+i)*(8-3*i)

norm 369

12+15*i = i*3*(5-4*i)
15+12*i = 3*(5+4*i)

norm 370

3+19*i = (1+i)*(2+i)*(6+i)
9+17*i = (1+i)*(2+i)*(6-i)
17+9*i = (1+i)*(2-i)*(6+i)
19+3*i = (1+i)*(2-i)*(6-i)

norm 373

7+18*i (p)
18+7*i (p)

norm 377

4+19*i = i*(3-2*i)*(5+2*i)
11+16*i = (3+2*i)*(5+2*i)
16+11*i = i*(3-2*i)*(5-2*i)
19+4*i = (3+2*i)*(5-2*i)

norm 386

5+19*i = (1+i)*(12+7*i)
19+5*i = (1+i)*(12-7*i)

norm 388

8+18*i = (1+i)²*(9-4*i)
18+8*i = -i*(1+i)²*(9+4*i)

norm 389

10+17*i (p)
17+10*i (p)

norm 392

14+14*i = -i*(1+i)³*7

norm 394

13+15*i = (1+i)*(14+i)
15+13*i = (1+i)*(14-i)

norm 397

6+19*i (p)
19+6*i (p)

norm 400

12+16*i = -(1+i)⁴*(2+i)²
16+12*i = -i*(1+i)⁴*(2-i)²
20 = -(1+i)⁴*(2+i)*(2-i)

norm 401

1+20*i (p)
20+i (p)

norm 404

2+20*i = (1+i)²*(10-i)
20+2*i = -i*(1+i)²*(10+i)

norm 405

9+18*i = i*(2-i)*3²
18+9*i = (2+i)*3²

norm 409

3+20*i (p)
20+3*i (p)

norm 410

7+19*i = i*(1+i)*(2-i)*(5-4*i)
11+17*i = (1+i)*(2-i)*(5+4*i)
17+11*i = (1+i)*(2+i)*(5-4*i)
19+7*i = -i*(1+i)*(2+i)*(5+4*i)

norm 416

4+20*i = -(1+i)⁵*(3+2*i)
20+4*i = -(1+i)⁵*(3-2*i)

norm 421

14+15*i (p)
15+14*i (p)

norm 424

10+18*i = -i*(1+i)³*(7+2*i)
18+10*i = -i*(1+i)³*(7-2*i)

norm 425

5+20*i = i*(2+i)*(2-i)*(4-i)
8+19*i = (2+i)²*(4+i)
13+16*i = i*(2-i)²*(4+i)
16+13*i = (2+i)²*(4-i)
19+8*i = i*(2-i)²*(4-i)
20+5*i = (2+i)*(2-i)*(4+i)

norm 433

12+17*i (p)
17+12*i (p)

norm 436

6+20*i = (1+i)²*(10-3*i)
20+6*i = -i*(1+i)²*(10+3*i)

norm 441

21 = 3*7

norm 442

1+21*i = i*(1+i)*(3-2*i)*(4-i)
9+19*i = (1+i)*(3+2*i)*(4-i)
19+9*i = (1+i)*(3-2*i)*(4+i)
21+i = -i*(1+i)*(3+2*i)*(4+i)

norm 445

2+21*i = i*(2+i)*(8-5*i)
11+18*i = (2+i)*(8+5*i)
18+11*i = i*(2-i)*(8-5*i)
21+2*i = (2-i)*(8+5*i)

norm 449

7+20*i (p)
20+7*i (p)

norm 450

3+21*i = i*(1+i)*(2-i)²*3
15+15*i = (1+i)*(2+i)*(2-i)*3
21+3*i = -i*(1+i)*(2+i)²*3

norm 452

14+16*i = (1+i)²*(8-7*i)
16+14*i = -i*(1+i)²*(8+7*i)

norm 457

4+21*i (p)
21+4*i (p)

norm 458

13+17*i = (1+i)*(15+2*i)
17+13*i = (1+i)*(15-2*i)

norm 461

10+19*i (p)
19+10*i (p)

norm 464

8+20*i = -i*(1+i)⁴*(5-2*i)
20+8*i = -(1+i)⁴*(5+2*i)

norm 466

5+21*i = (1+i)*(13+8*i)
21+5*i = (1+i)*(13-8*i)

norm 468

12+18*i = (1+i)²*3*(3-2*i)
18+12*i = -i*(1+i)²*3*(3+2*i)

norm 477

6+21*i = i*3*(7-2*i)
21+6*i = 3*(7+2*i)

norm 481

9+20*i = i*(3-2*i)*(6+i)
15+16*i = i*(3-2*i)*(6-i)
16+15*i = (3+2*i)*(6+i)
20+9*i = (3+2*i)*(6-i)

norm 482

11+19*i = (1+i)*(15+4*i)
19+11*i = (1+i)*(15-4*i)

norm 484

22 = -i*(1+i)²*11

norm 485

1+22*i = i*(2-i)*(9+4*i)
14+17*i = (2+i)*(9+4*i)
17+14*i = i*(2-i)*(9-4*i)
22+i = (2+i)*(9-4*i)

norm 488

2+22*i = -i*(1+i)³*(6+5*i)
22+2*i = -i*(1+i)³*(6-5*i)

norm 490

7+21*i = (1+i)*(2+i)*7
21+7*i = (1+i)*(2-i)*7

norm 493

3+22*i = i*(4+i)*(5-2*i)
13+18*i = i*(4-i)*(5-2*i)
18+13*i = (4+i)*(5+2*i)
22+3*i = (4-i)*(5+2*i)

norm 500

4+22*i = -i*(1+i)²*(2+i)³
10+20*i = (1+i)²*(2+i)*(2-i)²
20+10*i = -i*(1+i)²*(2+i)²*(2-i)
22+4*i = (1+i)²*(2-i)³

norm 505

8+21*i = i*(2-i)*(10+i)
12+19*i = i*(2-i)*(10-i)
19+12*i = (2+i)*(10+i)
21+8*i = (2+i)*(10-i)

norm 509

5+22*i (p)
22+5*i (p)

norm 512

16+16*i = (1+i)⁹

norm 514

15+17*i = (1+i)*(16+i)
17+15*i = (1+i)*(16-i)

norm 520

6+22*i = (1+i)³*(2-i)*(3-2*i)
14+18*i = -i*(1+i)³*(2-i)*(3+2*i)
18+14*i = -i*(1+i)³*(2+i)*(3-2*i)
22+6*i = -(1+i)³*(2+i)*(3+2*i)

norm 521

11+20*i (p)
20+11*i (p)

norm 522

9+21*i = (1+i)*3*(5+2*i)
21+9*i = (1+i)*3*(5-2*i)

norm 529

23 (p)

norm 530

1+23*i = (1+i)*(2+i)*(7+2*i)
13+19*i = (1+i)*(2+i)*(7-2*i)
19+13*i = (1+i)*(2-i)*(7+2*i)
23+i = (1+i)*(2-i)*(7-2*i)

norm 533

2+23*i = i*(3+2*i)*(5-4*i)
7+22*i = (3+2*i)*(5+4*i)
22+7*i = i*(3-2*i)*(5-4*i)
23+2*i = (3-2*i)*(5+4*i)

norm 538

3+23*i = (1+i)*(13+10*i)
23+3*i = (1+i)*(13-10*i)

norm 541

10+21*i (p)
21+10*i (p)

norm 544

12+20*i = -(1+i)⁵*(4+i)
20+12*i = -(1+i)⁵*(4-i)

norm 545

4+23*i = i*(2-i)*(10+3*i)
16+17*i = i*(2-i)*(10-3*i)
17+16*i = (2+i)*(10+3*i)
23+4*i = (2+i)*(10-3*i)

norm 548

8+22*i = (1+i)²*(11-4*i)
22+8*i = -i*(1+i)²*(11+4*i)

norm 549

15+18*i = i*3*(6-5*i)
18+15*i = 3*(6+5*i)

norm 554

5+23*i = (1+i)*(14+9*i)
23+5*i = (1+i)*(14-9*i)

norm 557

14+19*i (p)
19+14*i (p)

norm 562

11+21*i = (1+i)*(16+5*i)
21+11*i = (1+i)*(16-5*i)

norm 565

6+23*i = i*(2+i)*(8-7*i)
9+22*i = (2+i)*(8+7*i)
22+9*i = i*(2-i)*(8-7*i)
23+6*i = (2-i)*(8+7*i)

norm 569

13+20*i (p)
20+13*i (p)

norm 576

24 = i*(1+i)⁶*3

norm 577

1+24*i (p)
24+i (p)

norm 578

7+23*i = (1+i)*(4+i)²
17+17*i = (1+i)*(4+i)*(4-i)
23+7*i = (1+i)*(4-i)²

norm 580

2+24*i = (1+i)²*(2-i)*(5+2*i)
16+18*i = -i*(1+i)²*(2+i)*(5+2*i)
18+16*i = (1+i)²*(2-i)*(5-2*i)
24+2*i = -i*(1+i)²*(2+i)*(5-2*i)

norm 584

10+22*i = -i*(1+i)³*(8+3*i)
22+10*i = -i*(1+i)³*(8-3*i)

norm 585

3+24*i = i*(2+i)*3*(3-2*i)
12+21*i = (2+i)*3*(3+2*i)
21+12*i = i*(2-i)*3*(3-2*i)
24+3*i = (2-i)*3*(3+2*i)

norm 586

15+19*i = (1+i)*(17+2*i)
19+15*i = (1+i)*(17-2*i)

norm 592

4+24*i = -i*(1+i)⁴*(6-i)
24+4*i = -(1+i)⁴*(6+i)

norm 593

8+23*i (p)
23+8*i (p)

norm 596

14+20*i = (1+i)²*(10-7*i)
20+14*i = -i*(1+i)²*(10+7*i)

norm 601

5+24*i (p)
24+5*i (p)

norm 605

11+22*i = i*(2-i)*11
22+11*i = (2+i)*11

norm 610

9+23*i = i*(1+i)*(2-i)*(6-5*i)
13+21*i = (1+i)*(2-i)*(6+5*i)
21+13*i = (1+i)*(2+i)*(6-5*i)
23+9*i = -i*(1+i)*(2+i)*(6+5*i)

norm 612

6+24*i = (1+i)²*3*(4-i)
24+6*i = -i*(1+i)²*3*(4+i)

norm 613

17+18*i (p)
18+17*i (p)

norm 617

16+19*i (p)
19+16*i (p)

norm 625

7+24*i = -(2-i)⁴
15+20*i = (2+i)³*(2-i)
20+15*i = i*(2+i)*(2-i)³
24+7*i = -i*(2+i)⁴
25 = (2+i)²*(2-i)²

norm 626

1+25*i = (1+i)*(13+12*i)
25+i = (1+i)*(13-12*i)

norm 628

12+22*i = (1+i)²*(11-6*i)
22+12*i = -i*(1+i)²*(11+6*i)

norm 629

2+25*i = i*(4-i)*(6+i)
10+23*i = i*(4-i)*(6-i)
23+10*i = (4+i)*(6+i)
25+2*i = (4+i)*(6-i)

norm 634

3+25*i = (1+i)*(14+11*i)
25+3*i = (1+i)*(14-11*i)

norm 637

14+21*i = i*(3-2*i)*7
21+14*i = (3+2*i)*7

norm 640

8+24*i = i*(1+i)⁷*(2+i)
24+8*i = i*(1+i)⁷*(2-i)

norm 641

4+25*i (p)
25+4*i (p)

norm 648

18+18*i = -i*(1+i)³*3²

norm 650

5+25*i = (1+i)*(2+i)*(2-i)*(3+2*i)
11+23*i = (1+i)*(2+i)²*(3-2*i)
17+19*i = i*(1+i)*(2-i)²*(3-2*i)
19+17*i = -i*(1+i)*(2+i)²*(3+2*i)
23+11*i = (1+i)*(2-i)²*(3+2*i)
25+5*i = (1+i)*(2+i)*(2-i)*(3-2*i)

norm 653

13+22*i (p)
22+13*i (p)

norm 656

16+20*i = -i*(1+i)⁴*(5-4*i)
20+16*i = -(1+i)⁴*(5+4*i)

norm 657

9+24*i = i*3*(8-3*i)
24+9*i = 3*(8+3*i)

norm 661

6+25*i (p)
25+6*i (p)

norm 666

15+21*i = (1+i)*3*(6+i)
21+15*i = (1+i)*3*(6-i)

norm 673

12+23*i (p)
23+12*i (p)

norm 674

7+25*i = (1+i)*(16+9*i)
25+7*i = (1+i)*(16-9*i)

norm 676

10+24*i = -i*(1+i)²*(3+2*i)²
24+10*i = (1+i)²*(3-2*i)²
26 = -i*(1+i)²*(3+2*i)*(3-2*i)

norm 677

1+26*i (p)
26+i (p)

norm 680

2+26*i = -i*(1+i)³*(2+i)*(4+i)
14+22*i = -i*(1+i)³*(2+i)*(4-i)
22+14*i = -i*(1+i)³*(2-i)*(4+i)
26+2*i = -i*(1+i)³*(2-i)*(4-i)

norm 685

3+26*i = i*(2-i)*(11+4*i)
18+19*i = (2+i)*(11+4*i)
19+18*i = i*(2-i)*(11-4*i)
26+3*i = (2+i)*(11-4*i)

norm 689

8+25*i = i*(3-2*i)*(7+2*i)
17+20*i = (3+2*i)*(7+2*i)
20+17*i = i*(3-2*i)*(7-2*i)
25+8*i = (3+2*i)*(7-2*i)

norm 692

4+26*i = (1+i)²*(13-2*i)
26+4*i = -i*(1+i)²*(13+2*i)

norm 697

11+24*i = i*(4+i)*(5-4*i)
16+21*i = (4+i)*(5+4*i)
21+16*i = i*(4-i)*(5-4*i)
24+11*i = (4-i)*(5+4*i)

norm 698

13+23*i = (1+i)*(18+5*i)
23+13*i = (1+i)*(18-5*i)

norm 701

5+26*i (p)
26+5*i (p)

norm 706

9+25*i = (1+i)*(17+8*i)
25+9*i = (1+i)*(17-8*i)

norm 709

15+22*i (p)
22+15*i (p)

norm 712

6+26*i = -i*(1+i)³*(8+5*i)
26+6*i = -i*(1+i)³*(8-5*i)

norm 720

12+24*i = -i*(1+i)⁴*(2-i)*3
24+12*i = -(1+i)⁴*(2+i)*3

norm 722

19+19*i = (1+i)*19

norm 724

18+20*i = (1+i)²*(10-9*i)
20+18*i = -i*(1+i)²*(10+9*i)

norm 725

7+26*i = (2+i)²*(5+2*i)
10+25*i = i*(2+i)*(2-i)*(5-2*i)
14+23*i = i*(2-i)²*(5+2*i)
23+14*i = (2+i)²*(5-2*i)
25+10*i = (2+i)*(2-i)*(5+2*i)
26+7*i = i*(2-i)²*(5-2*i)

norm 729

27 = 3³

norm 730

1+27*i = i*(1+i)*(2-i)*(8-3*i)
17+21*i = (1+i)*(2+i)*(8-3*i)
21+17*i = (1+i)*(2-i)*(8+3*i)
27+i = -i*(1+i)*(2+i)*(8+3*i)

norm 733

2+27*i (p)
27+2*i (p)

norm 738

3+27*i = (1+i)*3*(5+4*i)
27+3*i = (1+i)*3*(5-4*i)

norm 740

8+26*i = (1+i)²*(2-i)*(6+i)
16+22*i = (1+i)²*(2-i)*(6-i)
22+16*i = -i*(1+i)²*(2+i)*(6+i)
26+8*i = -i*(1+i)²*(2+i)*(6-i)

norm 745

4+27*i = i*(2+i)*(10-7*i)
13+24*i = (2+i)*(10+7*i)
24+13*i = i*(2-i)*(10-7*i)
27+4*i = (2-i)*(10+7*i)

norm 746

11+25*i = (1+i)*(18+7*i)
25+11*i = (1+i)*(18-7*i)

norm 754

5+27*i = i*(1+i)*(3-2*i)*(5-2*i)
15+23*i = (1+i)*(3+2*i)*(5-2*i)
23+15*i = (1+i)*(3-2*i)*(5+2*i)
27+5*i = -i*(1+i)*(3+2*i)*(5+2*i)

norm 757

9+26*i (p)
26+9*i (p)

norm 761

19+20*i (p)
20+19*i (p)

norm 765

6+27*i = i*(2-i)*3*(4+i)
18+21*i = i*(2-i)*3*(4-i)
21+18*i = (2+i)*3*(4+i)
27+6*i = (2+i)*3*(4-i)

norm 769

12+25*i (p)
25+12*i (p)

norm 772

14+24*i = (1+i)²*(12-7*i)
24+14*i = -i*(1+i)²*(12+7*i)

norm 773

17+22*i (p)
22+17*i (p)

norm 776

10+26*i = -i*(1+i)³*(9+4*i)
26+10*i = -i*(1+i)³*(9-4*i)

norm 778

7+27*i = (1+i)*(17+10*i)
27+7*i = (1+i)*(17-10*i)

norm 784

28 = -(1+i)⁴*7

norm 785

1+28*i = i*(2+i)*(11-6*i)
16+23*i = (2+i)*(11+6*i)
23+16*i = i*(2-i)*(11-6*i)
28+i = (2-i)*(11+6*i)

norm 788

2+28*i = (1+i)²*(14-i)
28+2*i = -i*(1+i)²*(14+i)

norm 793

3+28*i = i*(3+2*i)*(6-5*i)
8+27*i = (3+2*i)*(6+5*i)
27+8*i = i*(3-2*i)*(6-5*i)
28+3*i = (3-2*i)*(6+5*i)

norm 794

13+25*i = (1+i)*(19+6*i)
25+13*i = (1+i)*(19-6*i)

norm 797

11+26*i (p)
26+11*i (p)

norm 800

4+28*i = -i*(1+i)⁵*(2-i)²
20+20*i = -(1+i)⁵*(2+i)*(2-i)
28+4*i = i*(1+i)⁵*(2+i)²

norm 801

15+24*i = i*3*(8-5*i)
24+15*i = 3*(8+5*i)

norm 802

19+21*i = (1+i)*(20+i)
21+19*i = (1+i)*(20-i)

norm 808

18+22*i = -i*(1+i)³*(10+i)
22+18*i = -i*(1+i)³*(10-i)

norm 809

5+28*i (p)
28+5*i (p)

norm 810

9+27*i = (1+i)*(2+i)*3²
27+9*i = (1+i)*(2-i)*3²

norm 818

17+23*i = (1+i)*(20+3*i)
23+17*i = (1+i)*(20-3*i)

norm 820

6+28*i = (1+i)²*(2+i)*(5-4*i)
12+26*i = -i*(1+i)²*(2+i)*(5+4*i)
26+12*i = (1+i)²*(2-i)*(5-4*i)
28+6*i = -i*(1+i)²*(2-i)*(5+4*i)

norm 821

14+25*i (p)
25+14*i (p)

norm 829

10+27*i (p)
27+10*i (p)

norm 832

16+24*i = -(1+i)⁶*(3-2*i)
24+16*i = i*(1+i)⁶*(3+2*i)

norm 833

7+28*i = i*(4-i)*7
28+7*i = (4+i)*7

norm 841

20+21*i = i*(5-2*i)²
21+20*i = (5+2*i)²
29 = (5+2*i)*(5-2*i)

norm 842

1+29*i = (1+i)*(15+14*i)
29+i = (1+i)*(15-14*i)

norm 845

2+29*i = -(2-i)*(3-2*i)²
13+26*i = i*(2-i)*(3+2*i)*(3-2*i)
19+22*i = i*(2+i)*(3-2*i)²
22+19*i = (2-i)*(3+2*i)²
26+13*i = (2+i)*(3+2*i)*(3-2*i)
29+2*i = -i*(2+i)*(3+2*i)²

norm 848

8+28*i = -i*(1+i)⁴*(7-2*i)
28+8*i = -(1+i)⁴*(7+2*i)

norm 850

3+29*i = (1+i)*(2+i)²*(4-i)
11+27*i = i*(1+i)*(2-i)²*(4-i)
15+25*i = (1+i)*(2+i)*(2-i)*(4+i)
25+15*i = (1+i)*(2+i)*(2-i)*(4-i)
27+11*i = -i*(1+i)*(2+i)²*(4+i)
29+3*i = (1+i)*(2-i)²*(4+i)

norm 853

18+23*i (p)
23+18*i (p)

norm 857

4+29*i (p)
29+4*i (p)

norm 865

9+28*i = i*(2-i)*(13+2*i)
17+24*i = i*(2-i)*(13-2*i)
24+17*i = (2+i)*(13+2*i)
28+9*i = (2+i)*(13-2*i)

norm 866

5+29*i = (1+i)*(17+12*i)
29+5*i = (1+i)*(17-12*i)

norm 872

14+26*i = -i*(1+i)³*(10+3*i)
26+14*i = -i*(1+i)³*(10-3*i)

norm 873

12+27*i = i*3*(9-4*i)
27+12*i = 3*(9+4*i)

norm 877

6+29*i (p)
29+6*i (p)

norm 881

16+25*i (p)
25+16*i (p)

norm 882

21+21*i = (1+i)*3*7

norm 884

10+28*i = (1+i)²*(3-2*i)*(4+i)
20+22*i = -i*(1+i)²*(3+2*i)*(4+i)
22+20*i = (1+i)²*(3-2*i)*(4-i)
28+10*i = -i*(1+i)²*(3+2*i)*(4-i)

norm 890

7+29*i = i*(1+i)*(2-i)*(8-5*i)
19+23*i = (1+i)*(2-i)*(8+5*i)
23+19*i = (1+i)*(2+i)*(8-5*i)
29+7*i = -i*(1+i)*(2+i)*(8+5*i)

norm 898

13+27*i = (1+i)*(20+7*i)
27+13*i = (1+i)*(20-7*i)

norm 900

18+24*i = -i*(1+i)²*(2+i)²*3
24+18*i = (1+i)²*(2-i)²*3
30 = -i*(1+i)²*(2+i)*(2-i)*3

norm 901

1+30*i = i*(4+i)*(7-2*i)
15+26*i = i*(4-i)*(7-2*i)
26+15*i = (4+i)*(7+2*i)
30+i = (4-i)*(7+2*i)

norm 904

2+30*i = -i*(1+i)³*(8+7*i)
30+2*i = -i*(1+i)³*(8-7*i)

norm 905

8+29*i = i*(2+i)*(10-9*i)
11+28*i = (2+i)*(10+9*i)
28+11*i = i*(2-i)*(10-9*i)
29+8*i = (2-i)*(10+9*i)

norm 909

3+30*i = i*3*(10-i)
30+3*i = 3*(10+i)

norm 914

17+25*i = (1+i)*(21+4*i)
25+17*i = (1+i)*(21-4*i)

norm 916

4+30*i = (1+i)²*(15-2*i)
30+4*i = -i*(1+i)²*(15+2*i)

norm 922

9+29*i = (1+i)*(19+10*i)
29+9*i = (1+i)*(19-10*i)

norm 925

5+30*i = i*(2+i)*(2-i)*(6-i)
14+27*i = (2+i)²*(6+i)
21+22*i = i*(2-i)²*(6+i)
22+21*i = (2+i)²*(6-i)
27+14*i = i*(2-i)²*(6-i)
30+5*i = (2+i)*(2-i)*(6+i)

norm 928

12+28*i = -(1+i)⁵*(5+2*i)
28+12*i = -(1+i)⁵*(5-2*i)

norm 929

20+23*i (p)
23+20*i (p)

norm 932

16+26*i = (1+i)²*(13-8*i)
26+16*i = -i*(1+i)²*(13+8*i)

norm 936

6+30*i = -i*(1+i)³*3*(3+2*i)
30+6*i = -i*(1+i)³*3*(3-2*i)

norm 937

19+24*i (p)
24+19*i (p)

norm 941

10+29*i (p)
29+10*i (p)

norm 949

7+30*i = i*(3-2*i)*(8+3*i)
18+25*i = (3+2*i)*(8+3*i)
25+18*i = i*(3-2*i)*(8-3*i)
30+7*i = (3+2*i)*(8-3*i)

norm 953

13+28*i (p)
28+13*i (p)

norm 954

15+27*i = (1+i)*3*(7+2*i)
27+15*i = (1+i)*3*(7-2*i)

norm 961

31 (p)

norm 962

1+31*i = (1+i)*(3+2*i)*(6+i)
11+29*i = (1+i)*(3+2*i)*(6-i)
29+11*i = (1+i)*(3-2*i)*(6+i)
31+i = (1+i)*(3-2*i)*(6-i)

norm 964

8+30*i = (1+i)²*(15-4*i)
30+8*i = -i*(1+i)²*(15+4*i)

norm 965

2+31*i = i*(2+i)*(12-7*i)
17+26*i = (2+i)*(12+7*i)
26+17*i = i*(2-i)*(12-7*i)
31+2*i = (2-i)*(12+7*i)

norm 968

22+22*i = -i*(1+i)³*11

norm 970

3+31*i = i*(1+i)*(2-i)*(9-4*i)
21+23*i = (1+i)*(2+i)*(9-4*i)
23+21*i = (1+i)*(2-i)*(9+4*i)
31+3*i = -i*(1+i)*(2+i)*(9+4*i)

norm 976

20+24*i = -i*(1+i)⁴*(6-5*i)
24+20*i = -(1+i)⁴*(6+5*i)

norm 977

4+31*i (p)
31+4*i (p)

norm 980

14+28*i = (1+i)²*(2-i)*7
28+14*i = -i*(1+i)²*(2+i)*7

norm 981

9+30*i = i*3*(10-3*i)
30+9*i = 3*(10+3*i)

norm 985

12+29*i = i*(2-i)*(14+i)
16+27*i = i*(2-i)*(14-i)
27+16*i = (2+i)*(14+i)
29+12*i = (2+i)*(14-i)

norm 986

5+31*i = (1+i)*(4+i)*(5+2*i)
19+25*i = (1+i)*(4-i)*(5+2*i)
25+19*i = (1+i)*(4+i)*(5-2*i)
31+5*i = (1+i)*(4-i)*(5-2*i)

norm 997

6+31*i (p)
31+6*i (p)

norm 1000

10+30*i = -i*(1+i)³*(2+i)²*(2-i)
18+26*i = (1+i)³*(2-i)³
26+18*i = -(1+i)³*(2+i)³
30+10*i = -i*(1+i)³*(2+i)*(2-i)²

norm 1009

15+28*i (p)
28+15*i (p)

norm 1010

7+31*i = (1+i)*(2+i)*(10+i)
13+29*i = (1+i)*(2+i)*(10-i)
29+13*i = (1+i)*(2-i)*(10+i)
31+7*i = (1+i)*(2-i)*(10-i)

norm 1013

22+23*i (p)
23+22*i (p)

norm 1017

21+24*i = i*3*(8-7*i)
24+21*i = 3*(8+7*i)

norm 1018

17+27*i = (1+i)*(22+5*i)
27+17*i = (1+i)*(22-5*i)

norm 1021

11+30*i (p)
30+11*i (p)

norm 1024

32 = -i*(1+i)¹⁰

norm 1025

1+32*i = -(2-i)²*(5-4*i)
8+31*i = i*(2-i)²*(5+4*i)
20+25*i = i*(2+i)*(2-i)*(5-4*i)
25+20*i = (2+i)*(2-i)*(5+4*i)
31+8*i = (2+i)²*(5-4*i)
32+i = -i*(2+i)²*(5+4*i)

norm 1028

2+32*i = (1+i)²*(16-i)
32+2*i = -i*(1+i)²*(16+i)

norm 1033

3+32*i (p)
32+3*i (p)

norm 1037

14+29*i = i*(4+i)*(6-5*i)
19+26*i = (4+i)*(6+5*i)
26+19*i = i*(4-i)*(6-5*i)
29+14*i = (4-i)*(6+5*i)

norm 1040

4+32*i = -i*(1+i)⁴*(2+i)*(3-2*i)
16+28*i = -(1+i)⁴*(2+i)*(3+2*i)
28+16*i = -i*(1+i)⁴*(2-i)*(3-2*i)
32+4*i = -(1+i)⁴*(2-i)*(3+2*i)

norm 1042

9+31*i = (1+i)*(20+11*i)
31+9*i = (1+i)*(20-11*i)

norm 1044

12+30*i = (1+i)²*3*(5-2*i)
30+12*i = -i*(1+i)²*3*(5+2*i)

norm 1049

5+32*i (p)
32+5*i (p)

norm 1053

18+27*i = i*3²*(3-2*i)
27+18*i = 3²*(3+2*i)

norm 1058

23+23*i = (1+i)*23

norm 1060

6+32*i = (1+i)²*(2-i)*(7+2*i)
22+24*i = (1+i)²*(2-i)*(7-2*i)
24+22*i = -i*(1+i)²*(2+i)*(7+2*i)
32+6*i = -i*(1+i)²*(2+i)*(7-2*i)

norm 1061

10+31*i (p)
31+10*i (p)

norm 1066

15+29*i = i*(1+i)*(3-2*i)*(5-4*i)
21+25*i = (1+i)*(3-2*i)*(5+4*i)
25+21*i = (1+i)*(3+2*i)*(5-4*i)
29+15*i = -i*(1+i)*(3+2*i)*(5+4*i)

norm 1069

13+30*i (p)
30+13*i (p)

norm 1073

7+32*i = i*(5-2*i)*(6+i)
17+28*i = i*(5-2*i)*(6-i)
28+17*i = (5+2*i)*(6+i)
32+7*i = (5+2*i)*(6-i)

norm 1076

20+26*i = (1+i)²*(13-10*i)
26+20*i = -i*(1+i)²*(13+10*i)

norm 1082

11+31*i = (1+i)*(21+10*i)
31+11*i = (1+i)*(21-10*i)

norm 1088

8+32*i = -(1+i)⁶*(4-i)
32+8*i = i*(1+i)⁶*(4+i)

norm 1089

33 = 3*11

norm 1090

1+33*i = (1+i)*(2+i)*(10+3*i)
19+27*i = (1+i)*(2+i)*(10-3*i)
27+19*i = (1+i)*(2-i)*(10+3*i)
33+i = (1+i)*(2-i)*(10-3*i)

norm 1093

2+33*i (p)
33+2*i (p)

norm 1096

14+30*i = -i*(1+i)³*(11+4*i)
30+14*i = -i*(1+i)³*(11-4*i)

norm 1097

16+29*i (p)
29+16*i (p)

norm 1098

3+33*i = (1+i)*3*(6+5*i)
33+3*i = (1+i)*3*(6-5*i)

norm 1105

4+33*i = i*(2-i)*(3+2*i)*(4-i)
9+32*i = (2+i)*(3+2*i)*(4+i)
12+31*i = i*(2+i)*(3-2*i)*(4-i)
23+24*i = (2+i)*(3+2*i)*(4-i)
24+23*i = i*(2-i)*(3-2*i)*(4+i)
31+12*i = (2-i)*(3+2*i)*(4+i)
32+9*i = i*(2-i)*(3-2*i)*(4-i)
33+4*i = (2+i)*(3-2*i)*(4+i)

norm 1108

18+28*i = (1+i)²*(14-9*i)
28+18*i = -i*(1+i)²*(14+9*i)

norm 1109

22+25*i (p)
25+22*i (p)

norm 1114

5+33*i = (1+i)*(19+14*i)
33+5*i = (1+i)*(19-14*i)

norm 1117

21+26*i (p)
26+21*i (p)

norm 1124

10+32*i = (1+i)²*(16-5*i)
32+10*i = -i*(1+i)²*(16+5*i)

norm 1125

6+33*i = (2+i)³*3
15+30*i = i*(2+i)*(2-i)²*3
30+15*i = (2+i)²*(2-i)*3
33+6*i = i*(2-i)³*3

norm 1129

20+27*i (p)
27+20*i (p)

norm 1130

13+31*i = i*(1+i)*(2-i)*(8-7*i)
17+29*i = (1+i)*(2-i)*(8+7*i)
29+17*i = (1+i)*(2+i)*(8-7*i)
31+13*i = -i*(1+i)*(2+i)*(8+7*i)

norm 1138

7+33*i = (1+i)*(20+13*i)
33+7*i = (1+i)*(20-13*i)

norm 1145

11+32*i = i*(2-i)*(15+2*i)
19+28*i = i*(2-i)*(15-2*i)
28+19*i = (2+i)*(15+2*i)
32+11*i = (2+i)*(15-2*i)

norm 1152

24+24*i = i*(1+i)⁷*3

norm 1153

8+33*i (p)
33+8*i (p)

norm 1154

23+25*i = (1+i)*(24+i)
25+23*i = (1+i)*(24-i)

norm 1156

16+30*i = (1+i)²*(4-i)²
30+16*i = -i*(1+i)²*(4+i)²
34 = -i*(1+i)²*(4+i)*(4-i)

norm 1157

1+34*i = i*(3-2*i)*(8+5*i)
14+31*i = (3+2*i)*(8+5*i)
31+14*i = i*(3-2*i)*(8-5*i)
34+i = (3+2*i)*(8-5*i)

norm 1160

2+34*i = (1+i)³*(2-i)*(5-2*i)
22+26*i = -i*(1+i)³*(2+i)*(5-2*i)
26+22*i = -i*(1+i)³*(2-i)*(5+2*i)
34+2*i = -(1+i)³*(2+i)*(5+2*i)

norm 1165

3+34*i = i*(2+i)*(13-8*i)
18+29*i = (2+i)*(13+8*i)
29+18*i = i*(2-i)*(13-8*i)
34+3*i = (2-i)*(13+8*i)

norm 1168

12+32*i = -i*(1+i)⁴*(8-3*i)
32+12*i = -(1+i)⁴*(8+3*i)

norm 1170

9+33*i = i*(1+i)*(2-i)*3*(3-2*i)
21+27*i = (1+i)*(2-i)*3*(3+2*i)
27+21*i = (1+i)*(2+i)*3*(3-2*i)
33+9*i = -i*(1+i)*(2+i)*3*(3+2*i)

norm 1172

4+34*i = (1+i)²*(17-2*i)
34+4*i = -i*(1+i)²*(17+2*i)

norm 1181

5+34*i (p)
34+5*i (p)

norm 1184

20+28*i = -(1+i)⁵*(6+i)
28+20*i = -(1+i)⁵*(6-i)

norm 1186

15+31*i = (1+i)*(23+8*i)
31+15*i = (1+i)*(23-8*i)

norm 1189

10+33*i = i*(5+2*i)*(5-4*i)
17+30*i = (5+2*i)*(5+4*i)
30+17*i = i*(5-2*i)*(5-4*i)
33+10*i = (5-2*i)*(5+4*i)

norm 1192

6+34*i = -i*(1+i)³*(10+7*i)
34+6*i = -i*(1+i)³*(10-7*i)

norm 1193

13+32*i (p)
32+13*i (p)

References

External links

[1] ttp://oeis.org/classic/A001481

[2] ttp://oeis.org/classic/A055025

[3] ttp://oeis.org/classic/A103431

[4] ttp://oeis.org/classic/A103432

[1]

[2]

[3]

[4]

Nomenclature

Factorizations

See Also

References

External links