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On x^3+y^3+z^3=t^4

Source: Romanian TST 2000

July 28, 2010
number theorygreatest common divisornumber theory unsolved

Problem Statement

Prove that the equation x3+y3+z3=t4x^3+y^3+z^3=t^4 has infinitely many solutions in positive integers such that gcd⁡(x,y,z,t)=1\gcd(x,y,z,t)=1.
Mihai Pitticari & Sorin Rǎdulescu
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