yn+xn=zn

Solution for yn+xn=zn equation:

Simplifying
yn + xn = zn

Reorder the terms:
nx + ny = zn

Solving
nx + ny = nz

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1nz' to each side of the equation.
nx + ny + -1nz = nz + -1nz

Combine like terms: nz + -1nz = 0
nx + ny + -1nz = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(x + y + -1z) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0
Subproblem 2
Set the factor '(x + y + -1z)' equal to zero and attempt to solve:

Simplifying
x + y + -1z = 0

Solving
x + y + -1z = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + y + -1x + -1z = 0 + -1x

Reorder the terms:
x + -1x + y + -1z = 0 + -1x

Combine like terms: x + -1x = 0
0 + y + -1z = 0 + -1x
y + -1z = 0 + -1x
Remove the zero:
y + -1z = -1x

Add '-1y' to each side of the equation.
y + -1y + -1z = -1x + -1y

Combine like terms: y + -1y = 0
0 + -1z = -1x + -1y
-1z = -1x + -1y

Add 'z' to each side of the equation.
-1z + z = -1x + -1y + z

Combine like terms: -1z + z = 0
0 = -1x + -1y + z

Simplifying
0 = -1x + -1y + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}