01204211/homework6 number theory 1

This is part of 01204211-58

Due: TBA

H.1 (LPV-6.1.3) Prove that if $a|b$ and $a|c$, then $a|b+c$ and $a|b-c$.

H.2 (LPV-6.1.6) (a) Prove that for every integer $a$, $a-1|a^{2}-1$.

(b) More generally, prove that for every integer $a$ and positive integer $n$, $a-1|a^{n}-1$.

H.3 (LPV-6.3.3) Suppose that $a$ and $b$ are integers and $a|b$. Suppose that $p$ is a prime and $p|b$, but $p\not |a$. Prove that $p|(b/a)$.

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H.8