If a + b = c, then is a + b = c (mod n) for all n?(adsbygoogle = window.adsbygoogle || []).push({});

For example while reading LeVeque's Topics in Number Theory I came across a section on Fermat's Last Theorem in which he says: a way to show c^n = a^n + b^n has no solution is to assume the infinite amount of congruences c^n = a^n + b^n (mod p) for p = 2, 3, 5, 7, ... and then derive a contradiction.

I assume what he means is: if c^n = a^n + b^n, then c^n = a^n + b^n (mod n) for any n that we choose.

Is this valid?

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# Question on the mod operator.

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