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 statement3 of 7

$f_1(\{0\}, 1) = 0$ : can't represent $1$ with a single element from $\{0\}$ .

FormalConjectures/ErdosProblems/1192.leanErdos1192.erdos_1192.f_r_no_rep1 lineExact file

1Erdos1192.f_r {0} 1 1 = 0

TestStatement only, no proof