General Solution and Number of Solutions in Z5 Field for X+Y-Z=1 Equation

[transgalactic]

find a general solution and the number of solutions in Z5 field
of this equation:

X+Y-Z=1




i know i need to
y=0 z=1
y=1 z=0
but what next?

 

[Dick]

Z5? The integers mod 5? Then X and Y can be ANYTHING as long as you pick Z=X+Y-1, can't they? How many solutions is that?

 

[transgalactic]

z5 is mod 5

i need to find the global solution for that equation?

 

[Dick]

There are LOTS of solutions. 1+0-0=1, 1+3-3=1, 4+3-1=1, etc etc. Read my message again.

 

[transgalactic]

how to find a general solution?

 

[Dick]

Read my message #2 again. I told you.

 

[transgalactic]

so its (1-y+z,y,z)
i know that there is endless solutions
but doesn't mod 5 cuts them
into 5 solutions?

 

[Dick]

I would say you have 5 different values for Y and five different values for Z, then X is determined. How many possible (Y,Z) pairs?

 

[transgalactic]

25? possibilities

 

[Dick]

25? possibilities

That would be my answer.