The board / number theory / #208
Erdős Problem #208
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The sequence of squarefree numbers, denoted by `s` as in Erdős problem 208.
Let \(s_1 < s_2 < \dots\) be the sequence of squarefree numbers. Is it true that for any \(\epsilon > 0\) and large \(n\), \(s_{n+1} - s_n \ll_\epsilon s_n^\epsilon\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/208.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/208
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