{"id":"openai-math/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree","pdf":"https://github.com/openai/math/blob/main/preprints/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026/power-saving-intersective-polynomial-differences.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-power-saving-for-intersective-polynomial-differences-with-an-exponent-depending-only-on-the-degree-October-5-2026","tags":["additive-combinatorics","number-theory","polynomials"],"score":0,"title":"A power saving for intersective polynomial differences with an exponent depending only on the degree","domain":"Combinatorics","family":"182","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"An integer polynomial is intersective if it has a root modulo every positive integer. For each degree k ≥ 2, we prove that there is an exponent $`c_k\\gt 0`$ such that every set $`A\\subseteq\\{1,\\ldots,N\\}`$ whose differences avoid all nonzero values $`h(1),h(2),\\ldots`$, where h is an intersective polynomial of degree k with positive leading coefficient, satisfies $`|A|=O_h(N^{1-c_k})`$. The implied constant may depend on h , but the power-saving exponent depends only on its degree.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Power savings for intersective polynomial differences and prime arguments"}