### APMO 1989

Posted:

**Mon Apr 09, 2012 9:16 pm**How to crack this one ?

Prove that the equation

\[6(6a^2 + 3b^2 + c^2) = 5n^2\]

has no solutions in integers except $a = b = c = n = 0$.

Prove that the equation

\[6(6a^2 + 3b^2 + c^2) = 5n^2\]

has no solutions in integers except $a = b = c = n = 0$.