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a_{n+h}-a_n

Source: 36-th Vietnamese Mathematical Olympiad 1998

February 17, 2007
modular arithmeticalgebra unsolvedalgebra

Problem Statement

The sequence {an}n≥0\{a_{n}\}_{n\geq 0} is defined by a0=20,a1=100,an+2=4an+1+5an+20(n=0,1,2,...)a_{0}=20,a_{1}=100,a_{n+2}=4a_{n+1}+5a_{n}+20(n=0,1,2,...). Find the smallest positive integer hh satisfying 1998∣an+h−an∀n=0,1,2,...1998|a_{n+h}-a_{n}\forall n=0,1,2,...
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