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Logic & Puzzles

If 'p' is a prime number greater than 2 in a Diffie-Hellman key exchange, which consequence necessarily follows according to Fermat's Little Theorem?

A)a^(p-1) ≡ 0 (mod p) for all 'a'
B)a^p ≡ a (mod p) only if gcd(a,p)=1
C)a^(p+1) ≡ a (mod p) for all 'a'
D)a^(p-1) ≡ 1 (mod p) if gcd(a,p)=1

💡 Explanation

Fermat's Little Theorem dictates that if 'p' is prime and 'a' is coprime to 'p', then a^(p-1) is congruent to 1 (mod p), because this theorem directly relates to modular exponentiation. Therefore, option D is correct, rather than other options which misstate or modify the theorem’s conditions.

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