Hi,

Given the following three equations

$\displaystyle a=k^2(m^2-2mn-n^2)^2$

$\displaystyle b=k^2(m^2+n^2)^2$

$\displaystyle c=k^2(m^2+2mn-n^2)^2$

I can show programatically that a, b and c are always congruent MOD 24 for any of the $\displaystyle 24^3$ combinations of k, m and n MOD 24.

Is there a 'nicer', more mathematical method I can use to prove the same, rather than this 'sledgehammer' approach?

Thank you