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Various cases of Hensel’s lemma and its implications. The connection between solving congruences modulo prime powers and their solutions in the field of p-adic numbers. Estimates of the number of solutions modulo prime powers. The Minkowski-Hasse theorem and an introduction to the Local-Global principle. Problem Set 3: Hensel’s lemma for finding solutions of equations and congruences. Solving p-adic equations with SageMath.