Algebraic Number Theory
Mathematical induction is a proof technique used to establish the validity of a statement for all natural numbers. It involves two main steps: first, proving the base case, usually for the smallest natural number, and then showing that if the statement holds for an arbitrary natural number, it also holds for the next one. This method is particularly useful for problems involving sequences, series, and properties of numbers, including those relevant to famous conjectures and theorems.
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