Peter 25.05.2007 03:25 Show that any integer can be expressed as the form $a^{2}+b^{2}-c^{2}$, where $a, b, c \in \mathbb{Z}$.
nkouevda 24.09.2007 09:14 Let $ n = a^{2}+b^{2}-c^{2}$. Any odd integer can be expressed as the difference of two squares: $ 2m+1 = (m+1)^{2}-m^{2}$. If $ n$ is odd, then $ b = 0$ and $ n = 2a-1 = 2c+1$. If $ n$ is even, then $ b = 1$ and $ n = 2a = 2c+2$.