PPL 040 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 040Erdős Problem #126

Permanent problem IDPPL 040

Verified openErdősconjecture

Number theory

Erdős Problem #126

Let f(n) be maximal such that if A⊆ℕ has | A|=n then ∏_(a≠ b∈ A)(a+b) has at least f(n) distinct prime factors. Is it true that f(n)/log n→∈fty?

number theory
01

The problem

Let f(n) be maximal such that if A⊆ℕ has | A|=n then ∏_(a≠ b∈ A)(a+b) has at least f(n) distinct prime factors. Is it true that f(n)/log n→∈fty?

Open since1934source estimate
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$250Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

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Sources & reading