Solution to Problem 238

Correct solutions were submitted by Dan Dima, Ron Welch, Bill Webb, Nancy Schwarzkopf, Lou Cairoli and Jens Voß.

n=[(p-1)/2]! works.

We need to show that n² is congruent to -1 modulo p. Notice that

Since (p-1)/2 is even, this is (p-1)!, which is congruent to -1 modulo p by Wilson's Theorem.

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