The board / number theory / #364
Erdős Problem #364
VERIFIABLEdatabase updated 2025-08-31
Still open — but if it is true, a finite example proves it, so a computer search could in principle prove it. A search can't disprove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
There is no consecutive triple of 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/364.Prizenone
Topicsnumber theory, powerful
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/364
Attempts
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Exact from-scratch enumeration proves there is no square-centered powerful triple \(x^2-1,x^2,x^2+1\) for \(x\le10^{17}\) (center \(\le10^{34}\)); the unrestricted problem remains open because no unif
PARTIAL