# A single formula to express every positive integer with digits 0-9 in which every digit is used only once.

Ross Honsberger (*Mathematical Gems III*, MAA, 1985, p 175) credits Verner Hoggatt Jr. with the following formula

,

where there are exactly *n* square roots. If the fraction in the first base is written as

,

which is equivalent to

,

which, in turn, states the obvious

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