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infinite couple of a,b 2011 China national Olmypiad 6

Source:

January 16, 2011
modular arithmeticalgorithmnumber theoryprime numbersDivisibility

Problem Statement

Let m,nm,n be positive integer numbers. Prove that there exist infinite many couples of positive integer nubmers (a,b)(a,b) such that a+b| am^a+bn^b ,  \gcd(a,b)=1.
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