[ You can try your example equations. If you try 2x^{3}y^{2}
+ 4x^{2}y + 2xy - 500 = 0, the program will return 2 as the value of x and 5 as the value of y.
If you try 2x^{3}y^{2} + 4x^{2}y + 2xy - 1032 = 0, the program will return 3 as the value of x and 4 as the value of y.
You can enter any integer in an input field. * There are no lower & upper bounds for integral polynomials with 2 or more variables; therefore, the program may run for
ever on most examples. One of the undecidable integral polynomial is: 2x*^{3}y^{2}
+ 4x^{2}y + 2xy - 5 = 0 . Matiyasevich's theorem proves that multivariable integral polynomials are undecidable. ] Please send comments to: Pradip Peter Dey ( pdey@nu.edu)
For decidability of one-variable integral polynomials click here

For Rice's Theorem on Undecidability click here

For references click here