I am trying to solve an equation that I know has solutions, but what I am trying isn't working as expected, am I missing something? Here is the equation
Reduce[{160755614715009600 + 152 y^2 + 2630 z^2 ==
m (2567290440 + 152 y + 2630 z), y > 0, z > 0, m > 0}, {y, z,
m}, Integers]
Which gives me
(y | z | m) \[Element] Integers && y >= 1 && z >= 1 &&
m == (80377807357504800 + 76 y^2 + 1315 z^2)/(
1283645220 + 76 y + 1315 z)
Yet if I give the value for "m", I get a solution thus
Reduce[{160755614715009600 + 152 y^2 + 2630 z^2 ==
33395648 (2567290440 + 152 y + 2630 z), y > 0, z > 0}, {y,
z}, Integers]
Resulting in
(y == 37928418 && z == 1194380) || (y == 37928418 &&
z == 32201268) || (y == 46962630 &&
z == 2087228) || (y == 46962630 && z == 31308420)
Or am I expecting too much?
