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product of alpine numbers is alpine, when m divides 2^{2n+1} + 1

Source: Austrian Polish 2003 APMC

April 25, 2020
dividesdivisibleProductnumber theory

Problem Statement

A positive integer mm is alpine if mm divides 22n+1+12^{2n+1} + 1 for some positive integer nn. Show that the product of two alpine numbers is alpine.
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