Abstract

In this paper, we will study a partial sum modulus distribution for a specific natural number set using a dynamically sliding window. Then we will construct a cubic equation from this distribution and a formula to calculate this cubic equation zero. Then we will go through some applications of this Cubic equation using the basic algebraic concepts to explain the distribution of natural numbers.

First part in this paper, we will interduce a partial sums modulus distribution for natural numbers using a dynamic sliding window as a parameter to explore the natural numbers distribution. As a simpler way of studying the distribution of a multi dynamic subsets inside natural numbers domain.

Second part in this paper, we will interpret this distribution into a quadratic and cubic equations and twin cubic equation concept clarification, then will use these two concepts to explain the distribution of zeros on the Zeta function strip line.

In the last part, we will go through some applications for this distribution one of them will be an example of getting prime number factors using a partial sum of specific series of odd numbers.

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