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Old 2017-12-28, 12:48   #2
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Dec 2012
The Netherlands

32008 Posts

Originally Posted by carpetpool View Post
Bottom line, factor a^(p-1)-1 into irreducible polynomials I, and one of these polynomials when evaluated at a will be a multiple of p, if a is not 0 (mod p).
For any prime number \(p\), in the ring of polynomials with coefficients in the integers modulo \(p\) we have
\[ X^{p-1}-1=(X-1)(X-2)(X-3)\ldots (X-(p-1)). \]
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