53. (USA 2) Find all pairs of integers \(a\) and \(b\) for which 
\[ 7a + 14b = 5a^2 + 5ab + 5b^2 \]
53. The discriminant of the given equation considered as a quadratic equation in $b$ is $196-75 a^{2}$. Thus $75 a^{2} \leq 196$ and hence $-1 \leq a \leq 1$. Now the integer solutions of the given equation are easily found: $(-1,3),(0,0),(1,2)$.