Problem Statement
Let $F(N)$ be the size of the largest Sidon subset of $\{1,\ldots,N\}$. Is it true that for every $k\geq 1$ we have\[F(N+k)\leq F(N)+1\]for all sufficiently large $N$?
Categories:
Additive Combinatorics Sidon Sets
Progress
This may even hold with $k\approx \epsilon N^{1/2}$.Source: erdosproblems.com/155 | Last verified: January 13, 2026