Erdős Problem #939
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).
A set `S` belongs to `Erdos939Sums r` if it meets the following criteria: - The elements are positive. `0` has no prime factors, so it is vacuously `r`-powerful, and the source means positive integers. - The size of the set is `\(|S| = r - 2\)`. - The elements of the set are coprime (their greatest common divisor is 1). - Every element in `S` is an `\(r\)-powerful` number. - The sum of the elements in `S`, i.e., `\(\sum_{s \in S} s\)`, is also an `\(r\)-powerful` number. The summands are taken to be dis
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(d) no coprime 4-powerful solution \(a+b=c\) has \(\max(a,b)\leq10^{16}\), a 100-fold extension of the live bound; (a) the \(r\geq6\) infinite construction is independently proved, leaving global \(r=
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