Erdős Problem #43
Prior state unknown→disproved
both proposed bounds fail
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number-theory / Number Theory, Sidon Sets
Erdős Problem #43
If Sidon sets $A, B \subseteq \{1, \dots, N\}$ satisfy $(A-A) \cap (B-B) = \{0\}$, must $\binom{|A|}{2} + \binom{|B|}{2} \le \binom{f(N)}{2} + O(1)$, where $f(N)$ is the largest Sidon-set size in $[N]$ - and can the bound be improved by a fixed proportion when $|A| = |B|$?
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If Sidon sets $A, B \subseteq \{1, \dots, N\}$ satisfy $(A-A) \cap (B-B) = \{0\}$, must $\binom{|A|}{2} + \binom{|B|}{2} \le \binom{f(N)}{2} + O(1)$, where $f(N)$ is the largest Sidon-set size in $[N]$ - and can the bound be improved by a fixed proportion when $|A| = |B|$?
both proposed bounds fail
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