I know that, by definition, n|m implies m=pn for which p is an integer, but I don't know how to get n ≤ m.
2025-01-12 19:23:58.1736709838
Suppose m, n ∈ N. Explain why n|m implies n ≤ m.
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Assuming everything is positive, just note that $k\cdot n \ge n$ for positive integers $k$. (That's just saying that "Multiplying by a number by something bigger than one makes it bigger.")
Of course it breaks if you allow $n$ to divide $-n$, for example.