Putnam 1971 A4

A-4. Show that for $0<\varepsilon<1$ the expression $(x+y)^{n}\left(x^{2}-(2-\varepsilon) x y+y^{2}\right)$ is a polynomial with positive coefficients for $n$ sufficiently large and integral. For $\varepsilon=.002$ find the smallest admissible value of $n$.