A relevant point, perhaps, is that polynomials over Z/25Z do not form
a unique factorization domain (or even a domain) so even the
definition of what factors you might want to see is unclear.
Following Nils, for a prime power modulus, a sensible definition is to
take an approximation of the p-adic factorization. The for a general
modulus the Chinese remainder theorem is probably relevant.
To illustrate my non-uniqueness point, modulo 8 we have x^2-1 =
(x+1)(x-1) = (x-3)(x+3).
John Cremona
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