Problem Statement

A Fermat pseudoprime is a positive composite integer that passes the Fermat primality test. Fermat's little theorem states that if p is prime and a is coprime to p, then ap−1 − 1 is divisible by p. For an integer a > 1, if a composite integer x evenly divides ax−1 − 1, then x is called a Fermat pseudoprime to base a. Fermat pseudoprimes to base 2 are sometimes called Sarrus numbers or Poulet numbers. Fermat pseudoprimes can be found to any positive integer base. When using a base integer a = 1, this method returns all composite numbers.

For base integers a of 1 through 20:

Let's start with the solution:

fermat=. {{1 = x (y&|@^) <: y}}"0

(>: i. 20) ([ ,. fermat/ (# , 20&{.)@# ]) (#~ 0&p:) >: i. 50000