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Question 2: Show that the set I of all integers with binary operation, defined as a.b = a + b + 1, for all a, b belonging to I is an abelian group. Discrete Fourier transforms and function transforms in general require a good grasp of algebra, including the part that overlaps with "number theory". Paolo Ruffini was the first person to develop the theory of permutation groups, and like his predecessors, also in the context of solving algebraic equations.

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