Two simple remarks: The polynomial $x^k-1$ can be factorised over the integers as a product of (irreducible) Cyclotomic polynomials: $$x^k-1 = \prod_{d|k}\Phi_d(x).$$ If we choose $k$ to be a number ...
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Why can’t you use cyclotomic polynomials to factor big numbers really quickly? – mathoverflow.net
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