erdos_straus_conjecture

⚠️ Retired — specification defect

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

Erdős–Straus Conjecture: For every integer $n \geq 2$, the fraction $\frac{4}{n}$ can be written as a sum of three unit fractions:

for positive integers $a, b, c$.

For example: $4/5 = 1/2 + 1/4 + 1/20$; $4/7 = 1/2 + 1/15 + 1/210$.

Proposed by Erdős and Straus in 1948. Verified for all $n \leq 10^{14}$ (Swett). The formal statement expresses $4/n = 1/a + 1/b + 1/c$ as $4bc = n(bc + ac + ab)$ to avoid rational arithmetic.

Why this node was retired

The posted statement is

theorem erdos_straus_conjecture (n : ℕ) (hn : 2 ≤ n) :
    ∃ a b c : ℕ, 0 < a ∧ 0 < b ∧ 0 < c ∧
      4 * b * c = n * (b * c + a * c + a * b) := by
  sorry

Clearing denominators drops the factor a from the left side.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Replace4bc with4ab*c: 4abc=n(bc+ac+ab).

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.