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n is prime if 2^{n-1}-1 and not 2^h-1 is divisible by n, where n = ph + 1

Source: 15th -b QEDMO problem 9 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

May 30, 2021
number theorydivisible

Problem Statement

Let pp be a prime number and hh be a natural number smaller than pp. We set n=ph+1n = ph + 1. Prove that if 2n−1−12^{n-1}-1, but not 2h−12^h-1, is divisible by nn, then nn is a prime number.
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