I have the following quadratic diophantine of three variables: (4x^2 + 1 )( 4y^2 + 1 ) = (4z^2 + 1) but cannot find a good algorithm or method for finding solutions. Any advice would be appreciated.

- Jun 25th 2012, 08:56 AMDiophantusHow to solve this three-variable quadratic Diophantine equation?
I have the following quadratic diophantine of three variables: (4x^2 + 1 )( 4y^2 + 1 ) = (4z^2 + 1) but cannot find a good algorithm or method for finding solutions. Any advice would be appreciated.

- Jun 27th 2012, 03:03 AMDeMathRe: How to solve this three-variable quadratic Diophantine equation?
Maybe you should try these replacements: $\displaystyle 4x^2+1=a$ and $\displaystyle 4y^2+1=b$.