Problem 42

Erdős Problem #42: declared status 'solved'. Formalized: yes. Let $M\geq 1$ and $N$ be sufficiently large in terms of $M$. Is it true that for every Sidon set $A\subset \{1,\ldots,N\}$ there is another Sidon set $B\subset \{1,\ldots,N\}$ of size $M$ such that $(A-A)\cap(B-B)=\{0\}$? Prize: no. Tags: additive combinatorics, number theory, sidon sets.