# Congruence proof

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Please provide a detailed solution to the following problem:

Let p be an odd prime and a such that (a, p) = 1. Show that the equation

x^2 = a (mod p^i)

has a solution for all i if it has a solution for i = 1. How many solutions are there?

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Â© BrainMass Inc. brainmass.com December 24, 2021, 8:05 pm ad1c9bdddf>https://brainmass.com/math/discrete-math/discrete-math-congruence-problem-246588