Abstract
We show that if A is a subset of {1, …, n} which has no pair of elements whose difference is equal to p − 1 with p a prime number, then the size of A is O(n(log log n)−c(log log log log log n)) for some absolute c > 0.
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Lucier, J. Difference sets and shifted primes. Acta Math Hung 120, 79–102 (2008). https://doi.org/10.1007/s10474-007-7107-1
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DOI: https://doi.org/10.1007/s10474-007-7107-1