combinatorics / Additive combinatorics
Let $f_3(N)$ be the least size forcing a set $A \subseteq \{1,\ldots,N\}$ to contain distinct $a,b,c$ with $a+b$, $a+c$ and $b+c$ all in $A$. The upper bound $f_3(N) \le 5N/8 + O(1)$ matches the standard construction $[N/8,N/4] \cup [N/2,N]$, so $f_3(N) = 5N/8 + O(1)$.
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Let $f_3(N)$ be the least size forcing a set $A \subseteq \{1,\ldots,N\}$ to contain distinct $a,b,c$ with $a+b$, $a+c$ and $b+c$ all in $A$. The upper bound $f_3(N) \le 5N/8 + O(1)$ matches the standard construction $[N/8,N/4] \cup [N/2,N]$, so $f_3(N) = 5N/8 + O(1)$.
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Let $f_3(N)$ be the least size forcing a set $A \subseteq \{1,\ldots,N\}$ to contain distinct $a,b,c$ with $a+b$, $a+c$ and $b+c$ all in $A$. The upper bound $f_3(N) \le 5N/8 + O(1)$ matches the standard construction $[N/8,N/4] \cup [N/2,N]$, so $f_3(N) = 5N/8 + O(1)$.
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