MathDB

18

Part of 2007 Pre-Preparation Course Examination

Problems(1)

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

Source: Romanian TST 2000

7/28/2010
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
number theorygreatest common divisornumber theory unsolved