Erdős problem 364 · problems.science

There is no consecutive triple of powerful numbers.

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3 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

364.lean

Retained formal statement2 of 3

Erdős [Er76d] conjectured a stronger statement: if $n_k$ is the $k$ th powerful number, then $n_{k+2} - n_k > n_k^c$ for some constant $c > 0$ .

[Er76d] Erdős, P., Problems and results on number theoretic properties of consecutive integers and related questions. Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975) (1976), 25-44.

FormalConjectures/ErdosProblems/364.leanErdos364.erdos_364.variants.strong2 linesExact file

1∃ c,2  ∃ (_ : c > 0), ∀ (k : ℕ), ↑(Nat.nth Nat.Powerful (k + 2)) - ↑(Nat.nth Nat.Powerful k) > ↑(Nat.nth Nat.Powerful k) ^ c

OpenStatement only, no proof

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