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2ab+1 | a^2 + b^2 + 1

Source: Iran 3rd round 2013 - Number Theory Exam - Problem 2

September 11, 2013
algebrapolynomialVietanumber theory proposednumber theoryVieta Jumping

Problem Statement

Suppose that a,ba,b are two odd positive integers such that 2ab+1∣a2+b2+12ab+1 \mid a^2 + b^2 + 1. Prove that a=ba=b. (15 points)
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