SymPy Gamma

diophantine (2*x**2+3*x*y-4*y**2-2)

$$\begin{align}&\mathrm{Solve~the~diophantine~equation~}2 x^{2} + 3 x y - 4 y^{2} - 2 = 0\\&\mathrm{where~}(x, y)\mathrm{~are~integers}\end{align}$$

diophantine (2*x**2+3*x*y-4*y**2-2)

x	y
$$\frac{\left(-45 + 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t}}{8} + \frac{\left(-45 - 7 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}}{8} - \frac{3 \sqrt{41} \left(- \left(-45 + 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(-45 - 7 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{328}$$	$$\frac{\sqrt{41} \left(- \left(-45 + 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(-45 - 7 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{82}$$
$$\frac{\left(45 - 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t}}{8} + \frac{\left(7 \sqrt{41} + 45\right) \left(320 \sqrt{41} + 2049\right)^{t}}{8} - \frac{3 \sqrt{41} \left(- \left(45 - 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(7 \sqrt{41} + 45\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{328}$$	$$\frac{\sqrt{41} \left(- \left(45 - 7 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(7 \sqrt{41} + 45\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{82}$$
$$\frac{\left(2049 - 320 \sqrt{41}\right)^{t} \left(8196 - 1280 \sqrt{41}\right)}{8} + \frac{\left(320 \sqrt{41} + 2049\right)^{t} \left(1280 \sqrt{41} + 8196\right)}{8} - \frac{3 \sqrt{41} \left(- \left(2049 - 320 \sqrt{41}\right)^{t} \left(8196 - 1280 \sqrt{41}\right) + \left(320 \sqrt{41} + 2049\right)^{t} \left(1280 \sqrt{41} + 8196\right)\right)}{328}$$	$$\frac{\sqrt{41} \left(- \left(2049 - 320 \sqrt{41}\right)^{t} \left(8196 - 1280 \sqrt{41}\right) + \left(320 \sqrt{41} + 2049\right)^{t} \left(1280 \sqrt{41} + 8196\right)\right)}{82}$$
$$\frac{\left(-8196 + 1280 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t}}{8} + \frac{\left(-8196 - 1280 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}}{8} - \frac{3 \sqrt{41} \left(- \left(-8196 + 1280 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(-8196 - 1280 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{328}$$	$$\frac{\sqrt{41} \left(- \left(-8196 + 1280 \sqrt{41}\right) \left(2049 - 320 \sqrt{41}\right)^{t} + \left(-8196 - 1280 \sqrt{41}\right) \left(320 \sqrt{41} + 2049\right)^{t}\right)}{82}$$