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

Any help anyone? Thanks before hand.

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- May 18th 2012, 04:02 AMSMADI need help solving this 3 variable equation
x^2+y^2+z^2=xyz-1

Any help anyone? Thanks before hand. - May 18th 2012, 05:18 AMPlatoRe: I need help solving this 3 variable equation
- May 18th 2012, 10:05 AMSMADRe: I need help solving this 3 variable equation
By solve I mean is there a solution, which I know there isn't, but i want to know how I can show that.

- May 18th 2012, 10:11 AMHallsofIvyRe: I need help solving this 3 variable equation
Solution to

**what**? A**problem**has a solution, not an equation! I suspect that this is the same problem that was posted on another board- in which it was specified that the problem was to find**integer**values of x, y, and z that satisfy this equation. - May 18th 2012, 10:17 AMPlatoRe: I need help solving this 3 variable equation
- May 18th 2012, 10:40 AMSylvia104Re: I need help solving this 3 variable equation
Let us assume that you want to find

**integers**that satisfy the equation.

A check on the parity of each side of the equation shows that if the equation is to work, exactly two of must be even. Suppose WLOG that is odd and are even. Then (the square of any odd integer always and (the square of any even integer is divisible by Hence the LHS On the other hand, and so the RHS Hence the LHS can never equal the RHS, so there are no integer solutions to your equation.