(left and right) inverse. For, first observe that the map must be injective: implies :

Distinct elements map to distinct elements, so the image consists of the same finite number of elements, and the map is necessarily surjective. Specifically, (namely multiplication by ) must map some element to , , so that is an inverse for .

Applications

The expansion of the reciprocal in any base can also act as a source of pseudo-random numbers,

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