FermatPsp — Mathlib

English

The same recurrence holds for F_n in the integers, i.e., F_{n+2} = F_{n+1}^2 − 2(F_n − 1)^2 in Z.

Русский

Та же рекуррентность выполняется для F_n в целых числах: F_{n+2} = F_{n+1}^2 − 2(F_n − 1)^2 в Z.

LaTeX

$$F_{n+2} = F_{n+1}^2 - 2\\,(F_n - 1)^2$$

Lean4

/-- `n` is a Fermat pseudoprime to base `b` if `n` is a probable prime to base `b` and is composite. By
this definition, all composite natural numbers are pseudoprimes to base 0 and 1. This definition
also permits `n` to be less than `b`, so that 4 is a pseudoprime to base 5, for example.
-/
def FermatPsp (n b : ℕ) : Prop :=
  ProbablePrime n b ∧ ¬n.Prime ∧ 1 < n

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