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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Claim. Every sufficiently large integer is the sum of at most three 2-powerful (squarefull) numbers, integers nn such that p∣np\mid n implies p2∣np^2\mid n. This is the case r=2r=2 of Problem 1107. The result is D. R. Heath-Brown, Ternary quadratic forms and sums of three square-full numbers, Séminaire de Théorie des Nombres, Paris 1986–87, Progress in Mathematics 75, Birkhäuser Boston (1988), 137–163. Only its publication year is known, so the page is dated to the start of 1988.

Covers. The case r=2r=2 only: every large integer is a sum of at most three 2-powerful numbers. Nothing is proved for r≥3r\geq3.

Acceptance. The site's curator, Thomas Bloom, marks Problem 941, whose statement is exactly this case, proved and credits this paper, as the Problem 941 claim page records; that credit is the reviewed evidence. The site's remark on Problem 1107, which the site labels OPEN, is not counted on its own. The volume is an edited seminar proceedings rather than a journal, so no refereed evidence is listed. The formal-conjectures statement file tags the case as a solved variant; a statement file is not a formalization.

Depends on. No other wiki page; the claim rests on the cited paper.