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Number Theory

Source: Polish Mathematical Olympiad 2016 P4- Final Round

April 8, 2016
number theoryDivisibilityorder of an elementauyesl

Problem Statement

Let k,nk, n be odd positve integers greater than 11. Prove that if there a exists natural number aa such that k∣2a+1, n∣2a−1k|2^a+1, \ n|2^a-1, then there is no natural number bb satisfying k∣2b−1, n∣2b+1k|2^b-1, \ n|2^b+1.
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