Erdős problem 940 · problems.science

Let $r \ge 3$ . Is it true that the set of integers which are the sum of at most $r$ $r$ -powerful numbers has density $0$ ?

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5 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

940.lean

Retained formal statement4 of 5

Heath-Brown [He88] has proved that all large numbers are the sum of at most three $2$ -powerful numbers.

[He88] Heath-Brown, D. R., Ternary quadratic forms and sums of three square-full numbers. (1988), 137--163.

FormalConjectures/ErdosProblems/940.leanErdos940.erdos_940.variants.three_powerful1 lineExact file

1∀ᶠ (x : ℕ) in Filter.atTop, ∃ S, S.card ≤ 3 ∧ (∀ s ∈ S, Nat.Full 2 s) ∧ x = S.sum

SolvedStatement only, no proof