Wall-Sun-Sun primes

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The Wall-Sun-Sun primes or Fibonacci-Wieferich primes are a class of prime numbers. A prime p > 5 is a Wall-Sun-Sun prime if $F_{p-({\frac {p}{5}})}\equiv 0{\pmod {p^{2}}}$, where F_i denotes the i-th Fibonacci number (A000045) and $({\tfrac {p}{5}})$ denotes the Legendre symbol. D. D. Wall in 1960 asked whether this congruence is impossible for all primes p > 5. Zhi Hong Sun and Zhi Wei Sun showed in 1992 that if the First Case of Fermat's last theorem is false for an odd prime p, then p is a Wall-Sun-Sun prime.

Sequences

A113649, A113650, A241014, A244801

See also

• Wieferich primes