If a is a square mod p . Then explain why “a^(p-1)/2≡1 (mod p)” is this...

Question

Question

If a is a square mod p . Then explain why “a^(p-1)/2≡1 (mod p)” is this true.

engineering Computer-Science

Answer 1

Answer #1

By using Fermat's Little Theorem

1 (mod p)

Now since a is a square, we can write it as b² for some b.

Substituting a^1/2 = b

a^(p-1)/2 1 (mod p)

Hence proved.

Answer 2

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