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 $m≥n+k$ ?

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8 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

686.lean

Retained formal statement6 of 8

Can every non-square $N≥2$ 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 $m≥n+k$ ?

FormalConjectures/ErdosProblems/686.leanErdos686.erdos_686.variants.non_square3 linesExact file

1True ↔2  ∀ N ≥ 2,3    ¬IsSquare N → ∃ k ≥ 2, ∃ n, ∃ m ≥ n + k, ↑N = ↑(∏ i ∈ Finset.Icc 1 k, (m + i)) / ↑(∏ i ∈ Finset.Icc 1 k, (n + i))

SolvedStatement only, no proof