Erdős problem 686 · problems.science

Can every integer $N≥2$ be written as $N=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}$ for some $k≥2$ and $m≥n+k$ ?

Workspace

Continue locally Open source Sign in to contribute

Open this exact Problem, source revision, and authority Repository in Workbench. This handoff does not clone, switch, upload, or execute anything.

Canvas

public preview

Source#686
→
ResultNone
→
Checks0

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

AI collaborating with humans
Erdős AI contributions wiki · 9 Aug, 2025-15 Mar, 2026
Machine
AlphaProof, Claude, Gemini Deep Think, GPT-5.2 Thinking, GPT-5.4 Thinking, Seed 2.0 Pro
People
Adenwalla, Stijn Cambie, Wouter van Doorn, Vjekoslav Kovač, Miklos, Nat Sothanaphan, Quanyu Tang, Terence Tao, vilc, Malek Zribi
Open the source record
Solved as stated, hidden constraints
GPT-Erdős
Open the source record