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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Why can’t you use cyclotomic polynomials to factor big numbers really quickly?
Cyclotomic Factoring is a class of integer factoring algorithms. It is based on the Euler congruence $x^{\varphi(n)}-1 \equiv 0 \mod n$. There are a few well known special cases.
The $p-1$-Pollard a …