9

Part of 2014 Ukraine Team Selection Test

Problems(1)

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

Source: Ukraine TST 2014 p9

m, n

be odd prime numbers. Find all pairs of integers numbers

a, b

for which the system of equations:

x^m+y^m+z^m=a

x^n+y^n+z^n=b

has many solutions in integers

x, y, z

number theoryprime numbersparameterizationDiophantine Equationsdiophantinesystem of equations