MathDB
x^m+y^m+z^m=a, x^n+y^n+z^n=b , 3parameter diophantine system

Source: Ukraine TST 2014 p9

April 30, 2020
number theoryprime numbersparameterizationDiophantine Equationsdiophantinesystem of equations

Problem Statement

Let m,nm, n be odd prime numbers. Find all pairs of integers numbers a,ba, b for which the system of equations: xm+ym+zm=ax^m+y^m+z^m=a, xn+yn+zn=bx^n+y^n+z^n=b has many solutions in integers x,y,zx, y, z.
Back to ProblemsView on AoPS