Composite Fermat number implies Poulet number

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Suppose is a nonnegative integer. Let be the Fermat number:




In particular, if is composite, then is a Poulet number.

Related facts


Given: A nonnegative integer , .

To prove: .

Proof: For any nonnegative integer , . Thus, .

Now, for a Fermat number , the order of modulo is precisely . From the above, we conclude that the order of modulo divides , so .