Congruence of squares
Congruence of squares In number theory, a congruence of squares modulo an integer n is an equality ... to factor the integer n: finding a congruence of squares modulo n is something ...
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Congruence of squares   (translated from French)
Congruence of squares In théorie of the numbers , one congruence of squares modulo one entirety N is an equality ... factorization the entirety N : to solve one congruence of squares modulo N is a ...
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Talk:Congruence of squares
Talk:Congruence of squares The claim that finding square roots in ...
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... Fermat's theorem on sums of two squares
... Fermat's theorem on sums of two squares Fermat's theorem on sums of two squares states that an odd prime $p\; ...\; The\; only\; if\; clause\; is\; trivial:\; the$squares modulo $4$ are $0\; ...\; Fermat\text{'}s\; theorem\; on\; sums\; of\; two$squares in 1747, when he was forty years ... of which is a sum of two squares, is itself a sum of two ...
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Quadratic sieve
... The algorithm attempts to set up a congruence of squares modulo n (the integer to be factorized ... collects information that may lead to a congruence of squares; and the data processing phase, where it ... matrix and solves it to obtain a congruence of squares. The data collection phase ...
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Quadratic screen   (translated from French)
... objective The algorithm tries to establish one congruence of squares modulo N (entirety to be factorized), which ... collates information which can lead to a congruence of squares; and the phase of calculation of the ... matrice and solves it to obtain a congruence of squares. This phase requires a ...
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Dixon's factorization method
... s method is based on finding a congruence of squares. Fermat's factorization algorithm finds such a congruence by selecting random or pseudo-random x values and hoping one satisfies the congruence: $x^2\backslash equiv\; y^2\backslash quad\; ...\; an\; impractically\; long\; time\; to\; find\; a$congruence of squares. Dixon's method is ...
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Talk:Pythagorean theorem
... results in a shape formed from the squares of the other two sides, which can ... in this article, and which speaks of squares of numbers that are the lengths of ... geometric version that speaks of areas of squares. The modern version is what I would ... the article page should show those three squares! Can someone provide one? OK, what's ... understand it first, the problem is not congruence, the problem is that you can ...
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Factorization of Dixon   (translated from French)
... Dixon is based on research of one congruence of squares . The naive method of search for such a congruence is the random selection of values X and to hope that that satisfies congruence: x^2\equiv y^2\quad ... a long impracticable time to find a congruence of squares. The method of Dixon ...
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List matters of the theory of the numbers   (translated from French)
... of Montgomery Modular Exponentiation Linear theorem of congruence Method of successive substitutions Theorem of the ... Euler Symbol of Legendre Lemma of Gauss Congruence of squares Formulate of Luhn Cryptanalyse MOD N Test ... Identity of Brahmagupta Identity of the four squares of Euler Theorem of the four squares of Lagrange Taxicab numbers Taxicab numbers ...
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