Wilson's Theorem in Disguise
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 .[more]
This Demonstration uses Mathematica's built-in function RecurrenceTable to generate the sequence and finds for which is an integer.[less]
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.