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TOT 2006 Fall - Junior O-Level p3 product of numbers is a^2 - b^2

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February 25, 2020
number theoryDifference

Problem Statement

(a) Prove that from 20072007 given positive integers, one of them can be chosen so the product of the remaining numbers is expressible in the form a2−b2a^2 - b^2 for some positive integers aa and bb. (2) (b) One of 20072007 given positive integers is 20062006. Prove that if there is a unique number among them such that the product of the remaining numbers is expressible in the form a2−b2a^2 - b^2 for some positive integers aa and bb, then this unique number is 20062006. (2)
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