Mathematics – Combinatorics
Scientific paper
2008-11-09
Mathematics
Combinatorics
5 pages, accepted to publish, Integers
Scientific paper
We show that with high probability a random set of size $\Theta(n^{1-1/k})$
of $\{1,...,n\}$ contains two elements $a$ and $a+d^k$, where $d$ is a positive
integer. As a consequence, we prove an analogue of S\'ark\"ozy-F\"urstenberg's
theorem for random set.
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