(p-1)! + 1

by v_Enhance, Nov 25, 2011, 7:56 AM

Find all primes $p$ such that $(p-1)!+1$ is a perfect power of $p$.

Comment

6 Comments

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This looks like Wilson's Theorem.

by djmathman, Nov 25, 2011, 3:56 PM

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Whoa I saw this problem at AMSP

Solution

by GlassBead, Nov 25, 2011, 8:16 PM

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@djmathman: Then you just get $(p-1)!+1 \equiv -1+1\equiv0\mod p$ which isn't very helpful.

by AwesomeToad, Nov 25, 2011, 11:03 PM

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Oh darn that's much nicer than my original solution.

by v_Enhance, Nov 26, 2011, 1:04 AM

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Hm, what about lifting?

by AwesomeToad, Nov 26, 2011, 3:08 AM

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^ That was my original solution :P

by v_Enhance, Nov 26, 2011, 3:10 AM

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