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

Largest Expression

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

$x^2+x$ is the largest.

Given that $x$ is in $(0,1)$, we may deduce that $x^2+x> x^2> x^3> x^4$ and also that $x^2+x> x^2+x^3 = x(x+x^2)$.

This problem is taken from the UKMT Mathematical Challenges.

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