A little number theory fun. I am given that $167^2 + 32^2 = 28913$, and I am asked to find integers $a$ and $b$, such that $a^2 + b^2 = 28913000$.
Here's my thought process so far:
Knowing that $1000 = 10^2 + 30^2$, I rewrote $28913000$ as $28913\times 1000$, and proceeded to multiply the sums of squares:
$$(167^2 + 32^2)(10^2 + 30^2).$$
However, after foiling, I ended up with the sum of $4$ squares, and cannot think of a way to just find two squares, $a$ and $b$.
Any help would be greatly appreciated!