wall_sun_sun_conjecture

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Wall-Sun-Sun prime conjecture (1992): There are no Fibonacci-Wieferich primes. No prime p has been found where p² divides both F_{p-1} and F_{p+1}. No such prime found up to 10^17.

Why this node was retired

The posted statement is

import Mathlib

theorem wall_sun_sun_conjecture :
    ∀ p : ℕ, Nat.Prime p →
      ¬ ((p^2 : ℕ) ∣ Nat.fib (p - 1) ∧ (p^2 : ℕ) ∣ Nat.fib (p + 1)) := by
  sorry

Simultaneous divisibility of both F_(p−1) and F_(p+1) is substituted for the single Legendre-symbol-selected Fibonacci index.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

For primes p≠2,5 use the index p−(p/5), where (p/5) is the Legendre symbol, and ask whether any such p satisfies p²∣F_(p−(p/5)).

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.