Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay