The board / number theory / #376
Erdős Problem #376
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Are there infinitely many \(n\) such that \({2n\choose n}\) is coprime to \(105\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/376.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA030979
Original pageerdosproblems.com/376
Attempts
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exact exhaustive enumeration gives 14,273 positive solutions through \(10^{100}\), extending the public \(10^{70}\) table by 12,900 verified values, but supplies no uniform infinitude argument.
PARTIAL