# Square of Wieferich prime is Poulet number

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## Statement

Suppose  is a Wieferich prime, i.e., a prime number such that:



Then,  is a Poulet number (also called Sarrus number), i.e., a Fermat pseudoprime to base 2.

## Proof

Given:  is a prime such that 

To prove: 

Proof: We have:



Thus,  divides . This gives that:



Combining this with the given information, we get that .