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n|2^n-2 for n=(2^(2p)-1)/3

Source: VJIMC 2002 1.2

July 16, 2021
number theoryDivisibilityprimes

Problem Statement

Let p>3p>3 be a prime number and n=22p−13n=\frac{2^{2p}-1}3. Show that nn divides 2n−22^n-2.
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