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There are $45$ boxes, each of which contains $N$ weapons. If he distributes all the weapons evenly to his $2026$ soldiers, he would have $2016$ weapons left over. What is the smallest positive value of $N$?

The answer here is $450$ and the problem is that I can't think of other ways to get to the answer other than trial and error. I would appreciate it if someone could give a better solution.

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    $\begingroup$ Aren't you searching for $N$ such that $45N \ \text{mod} \ 2026 \equiv 2016$? $\endgroup$ – Mattos May 8 at 10:25

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