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q is divisor of 2^{q-1}- 1 if q = \frac{4^p-1}{3}

Source: 15th -a QEDMO problem 10 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

May 30, 2021
number theorydivisordivides

Problem Statement

Let p>3p> 3 be a prime number and let q=4p−13q = \frac{4^p-1}{3}. Show that qq is a composite integer as well is a divisor of 2q−1−12^{q-1}- 1.
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