For every degree k≥2 there is c_k>0 such that, for each fixed intersective integer polynomial h of degree k with positive leading coefficient, every A⊆{1,…,N} avoiding nonzero differences h(m), m≥1, has |A|=O_h(N^{1−c_k}).
For every degree k≥2 there is c_k>0 such that, for each fixed intersective integer polynomial h of degree k with positive leading coefficient, every A⊆{1,…,N} avoiding nonzero differences h(m), m≥1, has |A|=O_h(N^{1−c_k}).
For every degree k≥2 there is c_k>0 such that, for each fixed intersective integer polynomial h of degree k with positive leading coefficient, every A⊆{1,…,N} avoiding nonzero differences h(m), m≥1, has |A|=O_h(N^{1−c_k}).
If correct, extends a fixed power saving from squares to every intersective polynomial, with an exponent depending only on degree.
Do all intersective polynomial difference-free sets admit a fixed power saving depending only on polynomial degree?
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OpenAI reports a degree-uniform power saving for intersective polynomial differences
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