Erdős Problem 1214

References:

• erdosproblems.com/1214
• [CoSc97] Corrales-Rodrigáñez, Capi and Schoof, René, The support problem and its elliptic analogue. J. Number Theory (1997) [Volume 64, Issue 2], 276--290.

theorem Erdos1214.erdos_1214 : True ↔ ∀ (x y : ℕ), x ≥ 1 → y ≥ 1 → (∀ n ≥ 1, {p : ℕ | Nat.Prime p ∧ p ∣ x ^ n - 1} = {p : ℕ | Nat.Prime p ∧ p ∣ y ^ n - 1}) → x = y

Let $x,y\geq 1$ be integers such that, for all $n\geq 1$, the set of primes dividing $x^{n}-1$ is equal to the set of primes dividing $y^n-1$. Must $x=y$?

Erdős asked this at a 1988 number theory conference in Banff.

A positive answer was given by Corrales-Rodrigáñez and Schoof [CoSc97].