Let p be a prime of the form 4k+3. Prove that either {(p-1)/2}!≡1 (mod p) or{(p-1)/2}!≡-1 (mod p)
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Originally Posted by jen_mojic Let p be a prime of the form 4k+3. Prove that either {(p-1)/2}!≡1 (mod p) or{(p-1)/2}!≡-1 (mod p) By Wilson's theorem we have, . Now, , and , and so on ... until the middle. Thus, . However, since . And therefore we have, . For example, let , then, Do the trick above, Thus, And the rest follows.
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