The board / number theory / #414
Erdős Problem #414
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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Let \(h_1(n) = h(n)\) and \(h_k(n) = h(h_{k-1}(n))\). Is it true, for any \(m,n\), there exist \(i\) and \(j\) such that \(h_i(m) = h_j(n)\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/414.Prizenone
Topicsnumber theory, iterated functions
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA064491
Original pageerdosproblems.com/414
Attempts
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Exact frontier computation proves coalescence for every pair of starts at most 10^10; the open uniform step is to force single-component square frontiers for arbitrarily large k.
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