The fundamental theorem underpins this difficulty because it means in the entire space of numbers, each number has but one set of prime factors.

He showed that in any set composed of integers—the positive and negative counting numbers—there’s a large subset of numbers that must be sum-free.

A structured list of 1,000 numbers might have a sumset with just 2,000 numbers in it. In the 1960s, a mathematician named Gregory Freiman began investigating sets with small sumsets in an effort to ...