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Least positive integer

Source: Indian RMO 2000 Problem 6

October 27, 2005

Problem Statement

(i) Consider two positive integers aa and bb which are such that aabba^a b^b is divisible by 20002000. What is the least possible value of abab? (ii) Consider two positive integers aa and bb which are such that abbaa^b b^a is divisible by 20002000. What is the least possible value of abab?
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