Equivalence of the k-SUM Hypothesis and the 3SUM Hypothesis

Determine whether the k-SUM Hypothesis, stated for all fixed k ≥ 3, is equivalent to the 3SUM Hypothesis (the special case k = 3).

Background

The paper adopts the standard k-SUM Hypothesis asserting that meet-in-the-middle time n^{⌈k/2⌉−o(1)} is optimal for each fixed k ≥ 3, which trivially implies the 3SUM Hypothesis for k = 3.

However, the authors point out that it is not currently known if the converse holds, i.e., whether hardness of 3SUM alone already implies hardness for all k.