Erdős problem 1192

Does there exist, for all $r\geq 2$ , a basis $A$ of order $r$ (so that $f_r(n)>0$ for all large $n$ ) such that $\sum_{n\leq x}f_r(n)^2 \ll x$ for all $x$ ?

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1192.lean

Retained formal statement5 of 7

The empty sum ( $r = 0$ ) gives exactly one representation of $0$ : the empty tuple.

FormalConjectures/ErdosProblems/1192.leanErdos1192.erdos_1192.f_r_zero_zero1 lineExact file

1∀ (A : Set ℕ), Erdos1192.f_r A 0 0 = 1

TestStatement only, no proof