Problem 941

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claims/: The 1 claim page of Problem 941, one per claimant's result; the problem's standing derives from them.

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Statement. Are all large integers the sum of at most three powerful numbers (i.e. if $p\mid n$ then $p^2\mid n$)?

Status. Proved.

Source. erdosproblems.com/941, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #941, https://www.erdosproblems.com/941.

References.

• [He88] Heath-Brown, D. R., Ternary quadratic forms and sums of three square-full numbers. Séminaire de Théorie des Nombres, Paris 1986–87, Progr. Math. 75, Birkhäuser Boston (1988), 137-163.
• [Er76d] Erdős, P., Problems and results on number theoretic properties of consecutive integers and related questions. Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975) (1976), 25-44.

Formalization. The statement appears without proof, tagged research solved, as erdos_940.variants.three_powerful in 940.lean and erdos_1107.variants.two in 1107.lean.

Progress

Not yet compiled.

Known Results

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