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arxiv: 0710.0644 · v2 · submitted 2007-10-02 · 🧮 math.CA · math.NT

Difference sets and the primes

classification 🧮 math.CA math.NT
keywords differenceabsoluteelementslessneverprimeprimessets
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Suppose that A is a subset of {1,...,N} such that the difference between any two elements of A is never one less than a prime. We show that |A| = O(N exp(-c(log N)^{1/4})) for some absolute c>0.

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