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Solving a diophantine equation!

Source: Iran 3rd round 2013 - Number Theory Exam - Problem 4

September 11, 2013
algebrapolynomialVietanumber theory proposednumber theoryDiophantine equationPell equations

Problem Statement

Prime p=n2+1p=n^2 +1 is given. Find the sets of solutions to the below equation: x2āˆ’(n2+1)y2=n2.x^2 - (n^2 +1)y^2 = n^2. (25 points)
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