Question: Prove that if a prime number p = 4n + 1, then if we denote N = (2n)!, then N^2 1 mod p Hint: Use

Prove that if a prime number p = 4n + 1, then if we denote N = (2n)!, then N^2 1 mod p

Hint: Use the fact that 1 2 . . .(2n) (2n + 1). . .(4n) = (4n)! 1 mod p and then rewrite numbers 4n, 4n 1, . . . , 2n + 1 as smaller remainders by mod 4n + 1.

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