Recall the following corollary to Fermat’s Little Theorem: If p is a prime, then a p ≡ a(mod p) for any integer a.
a. Use this result to prove the following lemma: If p and q are distinct primes with a^p ≡ a(mod q) and a^q ≡ a(mod p), then a^pq ≡ a(mod pq).
b. Use the result in part a. to establish that 2^340 ≡ 1(mod 341). Hence, the converse of Fermat’s Little Theorem is false
