Reference request for $\sum_{i=1}^\infty\left\lfloor\frac{n}{p^i}\right\rfloor$ The highest power of a prime $p$ that divides $n!$ is give by $p^{\left(\sum_{i=1}^\infty\left\lfloor\frac{n}{p^i}\right\rfloor\right)}$

I am fully aware of how to prove this but I don't have space to prove it in my dissertation. Therefore I need to reference it but I can't find it anywhere. I thought it would be easy to find as it's such a well known fact. Can anyone help?
The numerical example below could be an acceptable proof without words.

$$13!=1\cdot2\cdot\underline3\cdot4\cdot5\cdot\underline6\cdot7\cdot8\cdot\underline9\cdot10\cdot11\cdot\underline{12}\cdot13\to3\cdot6\cdot9\cdot12=3^4\cdot 4!$$
The numerical example below could be an acceptable proof without words.

$$13!=1\cdot2\cdot\underline3\cdot4\cdot5\cdot\underline6\cdot7\cdot8\cdot\underline9\cdot10\cdot11\cdot\underline{12}\cdot13\to3\cdot6\cdot9\cdot12=3^4\cdot 4!$$