SymPy Gamma

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

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

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

x	y
$$\frac{\left(-17 + 12 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t}}{4} + \frac{\left(-17 - 12 \sqrt{2}\right) \left(12 \sqrt{2} + 17\right)^{t}}{4} - \frac{1}{2}$$	$$\frac{\sqrt{2} \left(- \left(-17 + 12 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t} + \left(-17 - 12 \sqrt{2}\right) \left(12 \sqrt{2} + 17\right)^{t}\right)}{8}$$
$$\frac{\left(17 - 12 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t}}{4} + \frac{\left(12 \sqrt{2} + 17\right) \left(12 \sqrt{2} + 17\right)^{t}}{4} - \frac{1}{2}$$	$$\frac{\sqrt{2} \left(- \left(17 - 12 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t} + \left(12 \sqrt{2} + 17\right) \left(12 \sqrt{2} + 17\right)^{t}\right)}{8}$$
$$\frac{\left(-3 + 2 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t}}{4} + \frac{\left(-3 - 2 \sqrt{2}\right) \left(12 \sqrt{2} + 17\right)^{t}}{4} - \frac{1}{2}$$	$$\frac{\sqrt{2} \left(- \left(-3 + 2 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t} + \left(-3 - 2 \sqrt{2}\right) \left(12 \sqrt{2} + 17\right)^{t}\right)}{8}$$
$$\frac{\left(3 - 2 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t}}{4} + \frac{\left(2 \sqrt{2} + 3\right) \left(12 \sqrt{2} + 17\right)^{t}}{4} - \frac{1}{2}$$	$$\frac{\sqrt{2} \left(- \left(3 - 2 \sqrt{2}\right) \left(17 - 12 \sqrt{2}\right)^{t} + \left(2 \sqrt{2} + 3\right) \left(12 \sqrt{2} + 17\right)^{t}\right)}{8}$$