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diophantine: 2^x + 21^x = y^3 , 2^x + 21^y = z^2y

Source: IMAC Arhimede 2014 p3

May 6, 2019
number theoryDiophantine equationDiophantine Equations

Problem Statement

a) Prove that the equation 2x+21x=y32^x + 21^x = y^3 has no solution in the set of natural numbers. b) Solve the equation 2x+21y=z2y2^x + 21^y = z^2y in the set of non-negative integer numbers.
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