Hindman's finite sums and products conjecture asserts that, for every finite coloring of the positive integers and every positive integer 
, there is a 
-element set 
whose nonempty subset sums and
nonempty subset products all have the same color. Each
subset uses any member of 
at most once.
Hindman's Finite Sums and Products Conjecture
See also
Ramsey TheoryExplore with Wolfram|Alpha
References
Alweiss, R. "Monochromatic Sums and Products over
."
12 Jul 2026. https://arxiv.org/abs/2307.08901.
Cite this as:
Weisstein, Eric W. "Hindman's Finite Sums and Products Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HindmansFiniteSumsandProductsConjecture.html