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diophantine x^4 + p = 3y^4

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N1 day2

September 24, 2021
number theoryDiophantine equationdiophantine

Problem Statement

Let p>5p> 5 be a prime such that none of its digits is divisible by 33 or 77. Prove that the equation x4+p=3y4x^4 + p = 3y^4 does not have integer solutions.
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