(a) Let p be a prime and gcd(a,p)= 1. Use Fermat’s theorem to verify that x ≡ ap−2b(mod p) is a solution of the linear congruence ax ≡ b (mod p).
(b) By applying part (a), solve the congruences 2x≡ 1 (mod 31), 6x ≡ 5 (mod 11), and 3x ≡ 17 (mod 29).
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