Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)

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Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)

Let p be an odd prime and a an integer with p not dividing a. Show that a^(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)

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Add Answer to: Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)

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Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)