Problem Statement
Let $A$ be a finite Sidon set and $A+A=\{s_1<\cdots<s_t\}$. Is it true that\[\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2 \to \infty\]as $\lvert A\rvert\to \infty$?
Categories:
Sidon Sets
Progress
A similar problem can be asked for infinite Sidon sets.Source: erdosproblems.com/153 | Last verified: January 13, 2026