3 problems

The 3SUM problem asks whether, given $n$ integers from $\{-n^4,\ldots,+n^4\}$, there is a triple satisfying the 3SUM condition. 3SUM conjecture. The 3SUM problem on $n$ such intege…

Given a set $S$ of integers, let $n=|S|$. The 3SUM problem asks whether there are three integers $a,b,c\in S$ such that $a+b=c$. 3SUM Conjecture. Every algorithm solving 3SUM takes…

Given a set $A$ of $n$ numbers, determine whether there exist $a,b,c\in A$ such that $a+b+c=0$. The Integer 3SUM conjecture. The problem requires $\Omega(n^{2-o(1)})$ time, even wh…