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Problem 686 — Erdős Problems

Problem 686

Can every integer $N\geq 2$ be written as

N=\frac{\prod_{1\leq i\leq k}(m+i)}{\prod_{1\leq i\leq k}(n+i)}

for some $k\geq 2$ and $m\geq n+k$ ?

Source: erdosproblems.com/686

Number theory

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Er79d: Erdős, P., Some unconventional problems in number theory. Acta Math. Acad. Sci. Hungar. (1979), 71-80.

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Status: Open
Topics: Number theory
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