Wednesday, November 30th

Problem 
Find all naturals $a, b$ such that $\frac{a+1}{b}$ and $\frac{b+1}{a}$ are naturals.

Solution
The only possibilities are $a=b$ and $b=a+1$ (or $a=b+1$). Thus the only solutions are $(1,1)$, $(1,2)$ and $(2,3)$.