The board / number theory / #246
Erdős Problem #246
PROVED LEANdatabase updated 2025-12-28
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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The set \(\{a^k b^l : k,l \geq 0\}\).
Let \((a,b)=1\). The set \(\{a^kb^l: k,l\geq 0\}\) is complete - that is, every large integer is the sum of distinct integers of the form \(a^kb^l\) with \(k,l\geq 0\). We state the nontrivial case \(a,b\geq 2\), proved by Birch [Bi59].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/246.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/246
Attempts
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