Talk:Tonelli–Shanks algorithm

the case where p = 3 mod 4

It is written that in the special case where p equals 3 modulo 4, then the solution is simply:

$n^{(p+1)/4}$

I don't get why. Is it supposed to be obvious? --Grondilu (talk) 14:01, 20 June 2012 (UTC)

Yes. Square it, and apply Euler's criterion.—Emil J. 14:41, 20 June 2012 (UTC)

alberto tonelli needs enwiki biop (from itwiki)

Alberto Tonelli needs a enwiki translation. He has an article on the itwiki, a small one that doesn't mention he first came up with the important Tonelli-Shanks modular square root algorithm. There are three algorithms to take a modular square root and Tonelli's is as good as any of them. It's actually a rather important algorithm, since public key cryptography uses modular arithmetic. Endo999 (talk) 02:13, 28 August 2017 (UTC)

dickson's work on tonelli says the algorithm will work on mod p^k

I'm not a professional mathematician but I just read Dickson's "History of Numbers" where it says on page 215 that

A. Tonelli gave an explicit formula for the roots of $x^{2}=c(modp^{\lambda })$

Perhaps some mathematician should work out if the Tonelli algorithm takes modular square roots for powers of primes as well as for primes Endo999 (talk) 06:36, 30 August 2017 (UTC)