The board / number theory / #1107
Erdős Problem #1107
OPENdatabase updated 2025-11-17
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).
Helper Property: \(n\) is the sum of at most \(r+1\) numbers, each of which is \(r\)-full.
Let \(r \ge 2\). Is every large integer the sum of at most \(r + 1\) many \(r\)-powerful numbers?
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/1107.Prizenone
Topicsnumber theory, powerful
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1107
Attempts
submit one →Read our working report →
proved no fixed-modulus obstruction and exactly certified the stated finite suffixes through \(10^7\) for \(r=3\) and \(10^8\) for \(4\le r\le8\); eventual coverage for every \(r\ge3\) remains open.
PARTIAL