Problem

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Tags: number theory unsolved, number theory



Let $A$ be an infinite subset of $\mathbb{N}$, and $n$ a fixed integer. For any prime $p$ not dividing $n$, There are infinitely many elements of $A$ not divisible by $p$. Show that for any integer $m >1, (m,n) =1$, There exist finitely many elements of $A$, such that their sum is congruent to 1 modulo $m$ and congruent to 0 modulo $n$.