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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Closed form for sum of modulo remainders

Given a set of natural numbers {$N_1, ...N_n$} and another natural number $N$, find a closed form solution for the below sum $M = \sum_{i=1}^n N_i \% N$     where $N_i, N, n \in \mathbb N$     and $N …
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