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Wilson's Theorem in Disguise

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The American Mathematical Monthly problem 10578 considers a sequence defined by recurrence equation with initial conditions and asks to show that is only an integer for prime .

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This Demonstration uses Mathematica's built-in function RecurrenceTable to generate the sequence and finds for which is an integer.

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Contributed by: Oleksandr Pavlyk and Brett Champion (March 2011)
Open content licensed under CC BY-NC-SA

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It is easy to find a symbolic solution of the above recurrence equation:

The above fraction is an integer only for prime by virtue of Wilson's theorem.

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