OBM 1979 Problem 2

The remainder on dividing the polynomial $p(x)$ by $x^2 - (a+b)x + ab$ (where $a \not = b$ ) is $mx + n$ . Find the coefficients $m, n$ in terms of $a, b$ . Find $m, n$ for the case $p(x) = x^{200}$ divided by $x^2 - x - 2$ and show that they are integral.