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CIIM 2018 Problem 3

Source:

March 9, 2019
CIIM2018undergraduate

Problem Statement

Let mm be an integer and Zm\mathbb{Z}_m the set of integer modulo mm. An equivalence relation is defined in Zm\mathbb{Z}_m given by, x∼yx \sim y if there exists a natural tt such that y≡2tx ( mod m)y \equiv 2^tx \, (\bmod m) . Find al values of mm such that the number of equivalent classes is even.
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