Erdős #885 (?, AMS 11). STATEMENT: For integer $n \geq 1$ we define the factor difference set of $n$ by $D(n) = \{|a-b| : n=ab\}$. FORMAL: erdos_885: answer(sorry) ↔ ∀ k ≥ 1, ∃ Ns : Finset ℕ, (∀ n ∈ Ns, 1 ≤ n) ∧ Ns.card = k ∧ (⋂ n ∈ Ns, factorDifferenceSet n).ncard ≥ k; erdos_885: ∃ Ns : Finset ℕ, (∀ n ∈ Ns, 1 ≤ n) ∧ Ns.card = 2 ∧ (⋂ n ∈ Ns, factorDifferenceSet n).ncard ≥ 2; erdos_885: ∃ Ns : Finset ℕ, (∀ n ∈ Ns, 1 ≤ n) ∧ Ns.card = 3 ∧ KNOWN/REMARKS: # Erdős Problem 885 *References:* - erdosproblems.com/885 - [ErRo97] Erdős, P. and Rosenfeld, M., The factor-difference set of integers. (1997) - [Ji99] Jiménez-Urroz, J., A note on a conjecture of Erdős and {R}osenfeld. (1999) - [Br19] Bremner, A., On a problem of Erdős related to common factor differences. (2019) | Is it true that, for every $k \geq 1$, there exist integers $N_1 < \dots < N_k$ s RELATED: [] OEIS: []

id

vpr_8ef0d39bf9e2b019

frontier

Erdős problems frontier

kind

finding.add

created

2026-06-04