# There are $45$ boxes, each of which contains $N$ weapons. If he distributes all the weapons evenly to his $2026$ soldiers,

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.

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