Problem Statement
Does there exist a $k$ such that every sufficiently large integer can be written in the form\[\prod_{i=1}^k a_i - \sum_{i=1}^k a_i\]for some integers $a_i\geq 2$?
Categories:
Number Theory
Progress
Erdős attributes this question to Schinzel. Eli Seamans has observed that the answer is yes (with $k=2$) for a very simple reason:\[n = 2(n+2)-(2+(n+2)).\]There may well have been some additional constraint in the problem as Schinzel posed it, but [Er61] does not record what this is.Source: erdosproblems.com/493 | Last verified: January 15, 2026