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every divisors of 2n^2 - 1 gives a different remainder after division by 2n

Source: 2021 Dürer Math Competition Finals Day 1 E+5

January 2, 2022
number theoryremainderdivisor

Problem Statement

Let nn be a positive integer. Show that every divisors of 2n2āˆ’12n^2 - 1 gives a different remainder after division by 2n2n.
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