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Equation on rational numbers

Source: KMO 2022 P8

October 29, 2022
number theoryprime numbers

Problem Statement

pp is a prime number such that its remainder divided by 8 is 3. Find all pairs of rational numbers (x,y)(x,y) that satisfy the following equation. p2x4āˆ’6px2+1=y2p^2 x^4-6px^2+1=y^2
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