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Talk:Dixon's factorization method

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This is an old revision of this page, as edited by Decrypt3 (talk | contribs) at 20:47, 24 March 2006 (→Comment). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Comment

I cannot see a real difference to the Quadratic Sieve, but thar does not really matter.

Dixon's method is not a well-specified algorithm in that it doesn't really give a method for finding relations (presumably, brute-force search would be used). The quadratic sieve uses some mathematical facts and the sieving procedure to speed up the finding of relations. The number field sieve is yet another way of finding relations. Decrypt3 20:47, 24 March 2006 (UTC)[reply]

Question

I didn't understand this sentence: "This set of primes is called the factor base. Then, using the polynomial p(x) = x2 − n, many values of x are tested to see if p(x) factors completely over the factor base."

What is x? What is n? What does it mean to factor "over the factor base"?

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