# 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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##### Solution Summary

This provides a proof for a given congruence problem.

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