Show that expressing a positive integer into sum of four squares is not unique.
Consider the positive integer 169. We have
$$ 169 = 1^2 + 2^2 + 8^2 + 10^2 $$
$$ 169 = 2^2 + 4^2 + 7^2 + 10^2 $$
$$ 169 = 4^2 + 4^2 + 4^2 + 11^2 $$
$$ 169 = 4^2 + 5^2 + 8^2 + 8^2 $$
$$ 169 = 4^2 + 6^2 + 6^2 + 9^2 $$
And so we have shown that expressing a positive integer into a sum of four squares is not unique by providing a counter-example.