Square of Random Variable with t-Distribution has F-Distribution

Theorem
Let $k$ be a strictly positive integer.

Let $X \sim t_k$ where $t_k$ is the $t$-distribution with $k$ degrees of freedom.

Then:


 * $X^2 \sim F_{1, k}$

where $F_{1, k}$ is the F-distribution with $\tuple {1, k}$ degrees of freedom.