x^2+y^2+z^2=xyz-1
Any help anyone? Thanks before hand.
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.
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.