2 problems

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Local avoidance conjecture for polynomial images of integers and primes
Let $h\in\mathbb{Z}[x]$ be a nonzero polynomial, and let $X=h(\mathbb{Z})$ or $X=h(\mathcal{P})$ , where $\mathcal{P}$ denotes the set of primes. For each $m\in\mathbb{N}$ , let…
Conjectureopenadditive-combinatorics intersectivity polynomial-imagesarXiv posted 2 days ago
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Intersective sets contain a difference of two primes
Intersective prime-difference conjecture. For every intersective set $R$ ,
Conjectureopenadditive-combinatorics intersectivity prime-differencesarXiv posted 2 days ago

Local avoidance conjecture for polynomial images of integers and primes