Fermat pseudoprime

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Template:Base-relative pseudoprimality property This is not to be confused with Fermat prime

Definition

Suppose is a composite natural number and is relatively prime to . is termed a Fermat pseudoprime relative to base if we have:

.

In other words, divides , or, the order of mod divides .

Facts

Relation with other properties

Stronger properties

Property when applied to one or more choice of base

  • Carmichael number is a number that is a Fermat pseudoprime for every (relatively prime) base.
  • Poulet number is a Fermat pseudoprime to base (in particular, it needs to be an odd number).