Wilson's Theorem in Disguise

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .


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


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



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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.