3 Variable equation that i'm stuck on .

In summary, The given equation is a cubic Diophantine equation, which is known to be difficult to solve. The attempt at a solution involves considering the possibilities mod 2 and mod 4 on both sides of the equation, leading to the conclusion that the equation has no solution.
  • #1
mtayab1994
584
0

Homework Statement



Solve the following equation in N^3:

x^2+y^2+z^2=xyz-1



The Attempt at a Solution



I moved all the terms to one side, but I don't know what to do from there on.
 
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  • #2
That's a cubic Diophantine equation and those are notoriously difficult!
 
  • #3
Do you have any idea on how i can start it? I think i should make x=t and x=s as my two parameters and i'll get an equation in z. Is that a good idea?
 
  • #4
Consider the possibilities mod 2, then mod 4, on the two sides of the equation as originally given.
 
  • #5
Joffan said:
Consider the possibilities mod 2, then mod 4, on the two sides of the equation as originally given.

yea that's what i did i got lhs=1mod4 and rhs is -1mod4 thus this equation has no solution.
 

What is a 3 variable equation?

A 3 variable equation is an algebraic equation that contains three variables. This means that there are three unknown quantities in the equation that need to be solved for.

Why am I stuck on my 3 variable equation?

There are many reasons why someone may get stuck on a 3 variable equation. It could be due to a lack of understanding of the concept, a mistake in solving the equation, or a difficult combination of variables.

How do I solve a 3 variable equation?

To solve a 3 variable equation, you can use different methods such as substitution, elimination, or graphing. The specific method to use depends on the equation and the variables involved.

Can I use a calculator to solve a 3 variable equation?

Yes, you can use a calculator to solve a 3 variable equation. However, it is important to check your work and make sure the solution makes sense in the context of the problem.

What are the applications of 3 variable equations in real life?

3 variable equations are commonly used in physics, engineering, and economics to model complex systems and relationships. They are also used in data analysis and statistics to represent multiple variables that affect a certain outcome.

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