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

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Homework Help Overview

The discussion revolves around finding a general solution and the number of solutions for the equation X + Y - Z = 1 in the Z5 field, which refers to integers modulo 5.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between variables X, Y, and Z, questioning how many solutions exist given the constraints of the Z5 field. Some suggest that Z can be expressed in terms of X and Y, while others discuss the implications of modular arithmetic on the number of solutions.

Discussion Status

The discussion is active, with participants offering various interpretations of the problem and questioning the assumptions about the number of solutions. There is acknowledgment of the existence of multiple solutions, but no consensus on the exact count or method to determine them.

Contextual Notes

Participants note that the modular nature of the problem may limit the solutions, but the exact constraints and implications of Z5 are still being explored.

transgalactic
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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?
 
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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?
 
z5 is mod 5

i need to find the global solution for that equation?
 
There are LOTS of solutions. 1+0-0=1, 1+3-3=1, 4+3-1=1, etc etc. Read my message again.
 
how to find a general solution?
 
Read my message #2 again. I told you.
 
so its (1-y+z,y,z)
i know that there is endless solutions
but doesn't mod 5 cuts them
into 5 solutions?
 
Last edited:
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?
 
25? possibilities
 
  • #10
transgalactic said:
25? possibilities

That would be my answer.
 

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