7 Mar 2013

A Squared Prime Problem: Upper Secondary Mathematics Competitions

There are prime numbers p, such that the number squared p2 is a factor of [(p-1)! + 1].

For which of the following primes is this true?

2, 3, 5, 7, 11, 13, 17.

In a competition, without electronic devices, this question should take approximately 10 minutes. Doing the question by computer is trivial - although interesting as p becomes larger - the aim here is to find the fastest technique to do it manually, as if it were a test question.

You can post your answer in the Comments below, but please try it first!

Level: Upper Secondary (Red)

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