arXiv subjects

Brahim Mittou

Publications and source records attributed to Brahim Mittou.

2 recordsLinked to original sources

arXiv2026

A New Classification of Positive Integers Via New Divisor Functions

Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{τ(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $α$, we define and study some properties of two new divisor functions $σ_{e,α}$ and $σ_{o,α}$. The first computes the sum of the $α$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $α$-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↗

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 $T_p=\sum_{x\in\mathbb F_p}χ(x^3-x)$.

math.NT↗