1) Let $$\alpha$$ and $$\beta$$ be positive integers such that $$\alpha \beta +1$$ divides $$\alpha ^{2} + \beta ^{2}$$. Show that  $$\frac{\alpha ^{2} + \beta ^{2}}{ \alpha \beta +1}$$ is a square of some integer?
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2) Following the criteria of Euler infinite sum evaluation; can you give some value for this sum:
$$\sum_{n=0}^{\infty }{n} = 1+1+1+1+1+... = ??$$
$$3(x^2+y^2+z^2)=10(xy+yz+zx)$$