Erdős problem 1214 · problems.science

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 $x=y$ ?

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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].

FormalConjectures/ErdosProblems/1214.leanErdos1214.erdos_12142 linesExact file

1True ↔2  ∀ (x y : ℕ), x ≥ 1 → y ≥ 1 → (∀ n ≥ 1, {p | Nat.Prime p ∧ p ∣ x ^ n - 1} = {p | Nat.Prime p ∧ p ∣ y ^ n - 1}) → x = y

SolvedStatement only, no proof

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