If p is a prime number and if a ≡ 0 (mod p), then Fermat’s Little Theorem tells us that ap−1 ≡ 1 (mod p).
(a) The congruence 71734250 ≡ 1660565 (mod 1734251) is true. Can you conclude that 1734251 is a composite number?
(b) The congruence 12964026 ≡ 15179 (mod 64027) is true. Can you conclude that 64027 is a composite number?
(c) The congruence 252632 ≡ 1 (mod 52633) is true. Can you conclude that 52633 is a prime number?
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