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The p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems

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How do you prove that the series 5, 25, 625, ... can be continued forever to give a 10-adic ... [closed]

How do you prove that the series 5, 25, 625, ... can be continued forever to give a 10-adic solution to $n^2=n$? Here's a proof for a different solution (...1787109376): https://oeis.org/A018248/a01 …