arXiv subjects

Brahim Mittou

Publications and source records attributed to Brahim Mittou.

2 recordsLinked to original sources

arXiv2026

Exact Frequencies of Consecutive Quadratic Residue and Nonresidue Patterns Modulo a Prime

This paper determines the exact frequency of all consecutive sign patterns of lengths two and three formed by the quadratic character modulo an odd prime $p$. Using basic properties of character sums over finite fields, we derive exact counting formulas for pairs $(n, n+1)$ and triples $(n-1, n, n+1)$ exhibiting specific sequence patterns in $\{\pm 1\}$. The frequencies of pairs are classified entirely by $p \pmod 4$, whereas triples exhibit a more complex dependency on $p \pmod 8$ and the Jacobsthal sum $T_p=\sum_{x\in\mathbb F_p}\chi(x^3-x)$.

math.NT↗

arXiv2025

A New Classification of Positive Integers Via New Divisor Functions

Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{\tau(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $\alpha$, we define and study some properties of two new divisor functions $\sigma_{e,\alpha}$ and $\sigma_{o,\alpha}$. The first computes the sum of the $\alpha$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $\alpha$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive integers, namely, $k$-index ratio numbers and state three conjectures related to them.

math.GM↗