As a first goal, let's aim to find the variety associated with x^2 = 2 in the 7-adics. The solution is two base-7 numbers, extending infinitely to the left (similar to how \sqrt{2} extends infinitely to the right in the real numbers). The solutions are:

x_1 = ...4112011266421216213.

x_2 = ...2554655400245450454. = -x_1

Our goal is to reproduce these numbers.