New expansions for $x^n\pm y^n$ in terms of quadratic forms

Moustafa Ibrahim

We prove new theorems for the polynomial expansions of $x^n\pm y^n$ in terms of the binary quadratic forms $\alpha x^2+\beta xy+\alpha y^2$ and $a{x}^2+bxy+a{y}^2$. The paper gives new ari…