Hindman’s finite sums and products conjecture. Proves Hindman's finite sums and products conjecture: every finite coloring of the positive integers contains sets of any prescribed finite size whose nonempty subset sums and nonempty subset products all have one common color.
released 2026-09-23 | 2 theorems · 20 lemmas · 34 proofs · 35,053 words |
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We prove Hindman's finite sums and products conjecture: for every finite coloring of the positive integers and every positive integer k, there is a k-element set whose nonempty subset sums and nonempty subset products all have the same color.