Unique form to write any natural number

Question

I want to know if this is true, I have done many examples, but don't know how to prove it:

If $m \geq 1$ and $0 \leq k <m$, then, for any $n \in \mathbb{N}$, there is a unique $m$ and $k$ such that $$n=\frac{(m)(m-1)}{2}+k $$.

I have tried to show the limits that $n$ can take becouse of $k$, but I haven't come to nothing. Please help.

Answer 1

$\frac{m(m-1)}{2}$ is the sum of naturals from $0$ to $m-1$. Gaps between consecutive sums are of length $1,2,3,\dots,m-1$. Hope this helps.