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p^2 + q^2 + 49r^2 = 9k^2-101

Source: Mathematics Regional Olympiad of Mexico Center Zone 2018 P5

November 13, 2021
Diophantine equationdiophantinenumber theory

Problem Statement

Find all solutions of the equation p2+q2+49r2=9k2āˆ’101p ^ 2 + q ^ 2 + 49r ^ 2 = 9k ^ 2-101 with p p, qq and rr positive prime numbers and kk a positive integer.