N. Carella

collaborators

7 papers

math.GM2026

Linear Independence Of Some Irrational Numbers

N. A. Carella

This note presents an analytic technique for proving the linear independence of certain small subsets of real numbers over the rational numbers. The applications of this test produ…

math.NT2026

Simple Proof of the Primitive Root Conjecture

N. A. Carella

Let $u\neq \pm 1,v^2$ be a fixed integer, let $p\geq 2$ be a prime, and let $ord_{p} (u) ∣ p - 1$ be the multiplicative order of $u mod p$ . Define a prime countin…

math.GM2025

Small Prime $k$ th Power Residues and Nonresidues in Arithmetic Progressions

N. A. Carella

Let $p$ be a large odd prime, let $x = lo g p) (lo g lo g p)^{3 + ε}$ and let $q ≪ lo g lo g p$ be an integer, where $ε > 0$ is a small number. This note proves the exis…

math.GM2025

Upper Bound of the Least Quadratic Nonresidues

N. A. Carella

Let $p \geq 3$ be a large prime and let $n (p) \geq 2$ denotes the least quadratic nonresidue modulo $p$ . This note sharpens the standard upper bound of the least quadratic nonresidue f…

math.GM2025

Primitive Root Conjecture in Arithmetic Progressions

N. A. Carella

Let $x \geq 1$ be a large number, and let $1 \leq a < q$ be integers such that $g cd (a, q) = 1$ and $q = O (lo g^{c})$ with $c > 0$ constant. This note proves that the counting function for t…

math.NT2025

Small Primes And The Tau Function

N. A. Carella

This note shows that the prime values of the Ramanujan tau function $I ¨ (n) = \pm p$ misses every prime $p \leq 8.0 \times 1 0^{25}$ .

Linear Independence Of Some Irrational Numbers

Simple Proof of the Primitive Root Conjecture

Small Prime kth Power Residues and Nonresidues in Arithmetic Progressions

Upper Bound of the Least Quadratic Nonresidues

Primitive Root Conjecture in Arithmetic Progressions

Small Primes And The Tau Function

Small Prime $k$ th Power Residues and Nonresidues in Arithmetic Progressions