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China Northern Mathematical Olympiad 2013 , Problem 7

Source: China Xian

August 27, 2013
algebra proposedalgebraSequence

Problem Statement

Suppose that {an}\{a_n\} is a sequence such that an+1=(1+kn)an+1a_{n+1}=(1+\frac{k}{n})a_{n}+1 with a1=1a_{1}=1.Find all positive integers kk such that any ana_n be integer.
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