(a) Let a > 1 be an integer. Prove that any composite divisorof a ? 1 is a pseudoprime of base a.
(b) Suppose, for some m, than n divides a^(m ? 1) and n ? 1 (modm). Prove that if n is composite, then n is a pseudoprime of basea.
(c) Use (b) to give two examples pseudoprimes of base a with a =2 and a = 3 (hint: take m = 2k to be an even number).
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