The case of formula_41 corresponds to the "k"-Wall–Sun–Sun primes, for which Wall–Sun–Sun primes represent the special case "k" = 1. The "k"-Wall–Sun–Sun primes can be explicitly defined as primes "p" such that "p"2 divides the "k"-Fibonacci number formula_42, where "Fk"("n") = "Un"("k", −1) is a Lucas sequence of the first kind with discriminant "D" = "k"2 + 4 and formula_43 is the Pisano period of "k"-Fibonacci numbers modulo "p". For a prime "p" ≠ 2 and not dividing "D", this condition is equivalent to either of the following.