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$$\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$$
$$\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}$$
Note that F = ma is only true at sub-relativistic velocity. But $F = \frac{dp}{dt}$ is always true. As you apply arbitrarily large forces, you can get momentum as large as you like... but never infinite.