This article describes a sequence of natural numbers. The parameter for the sequence is a positive integer (or sometimes, nonnegative integer).
View other one-parameter sequences
This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers
Let be a nonnegative integer. The Fermat number, denoted , is defined as:
If it is prime, it is termed a Fermat prime.
- Composite Fermat number implies Poulet number: This states that any composite Fermat number is a Poulet number, i.e., a Fermat pseudoprime to base 2.
- Prime divisor of Fermat number is congruent to one modulo large power of two: For a Fermat number , any prime divisor is congruent to 1 mod , and for , congruen to 1 mod .
- Quadratic nonresidue equals primitive root for Fermat prime