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Cardinality of $\{ n_i + i^k: i \in \mathbb{N} \} \cap [1,T]$ where $\{n_i \}$ is all natural numbers in some order

Let $n_1, n_2, ...$ be a sequence of natural numbers such that $\{n_i: i \in \mathbb{N}\}$ as a set is all of natural numbers. Let $k$ be a positive integer. Is is possible to obtain a lower bound of ...
Johnny T.'s user avatar
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Infinite difference length of integer subsets

Let $A$ be a set of integers. In our recent researches, we've faced to the following property and definition: We say $A$ has infinite difference length, if (a) For every integer $n$ there exist a ...
M.H.Hooshmand's user avatar