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r + p^4 = q^4 diophantine

Source: Mathematics Regional Olympiad of Mexico Center Zone 2010 P5

November 10, 2021
number theoryDiophantine equationdiophantine

Problem Statement

Find all integer solutions (p,q,r)(p, q, r) of the equation r+p4=q4r + p ^ 4 = q ^ 4 with the following conditions: ∙\bullet rr is a positive integer with exactly 88 positive divisors. ∙\bullet pp and qq are prime numbers.
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