Question 167
We say that a positive integer $n$ is clever if there exist positive integers $a, b, c$ and $d$, not necessarily distinct, such that:
$$
n=\frac{a^{2}-b^{2}}{c^{2}+d^{2}}
$$
For example, 12 is clever, since:
$$
12=\frac{16^{2}-4^{2}}{4^{2}+2^{2}}
$$
Show that every positive integer is clever.
$$
n=\frac{a^{2}-b^{2}}{c^{2}+d^{2}}
$$
For example, 12 is clever, since:
$$
12=\frac{16^{2}-4^{2}}{4^{2}+2^{2}}
$$
Show that every positive integer is clever.