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Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the maximum of

$${1\over p} + {1\over q} + {1\over r}$$

where $p$, $q$ and $r$ are positive integers and

$${1\over p} + {1\over q} + {1\over r} < 1.$$

Prove that it is indeed a maximum.

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