Let $x,y\in \mathbb{N}$ and $k=\frac{x^2+y^2}{2xy+1}$. Determine all natural values of $k$.
Problem
Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade
Tags: algebra, Natural Number
Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade
Tags: algebra, Natural Number
Let $x,y\in \mathbb{N}$ and $k=\frac{x^2+y^2}{2xy+1}$. Determine all natural values of $k$.