Amirali Fatehizadeh

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math.NT2026

Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds

Amirali Fatehizadeh

For $n\ge2$, let $A(n)=π(n)-ω(n)$ and $B(n)=ϕ(n)-π(n)+ω(n)$ denote the numbers of prime and nonprime totatives of $n$, respectively, with $1$ included in $B(n)$. We con…

math.NT2026

On the Divisibility Relation $σ (n) ∣ σ (n + h)$ and a Generalized Erdős--Sierpiński Conjecture

Amirali Fatehizadeh, Florian Luca

For each fixed positive integer $h$ , we study the divisibility relation $σ (n) ∣ σ (n + h)$ . We isolate an explicit regular family arising from integral quotients of shifted abundancy…

math.NT2026

A generalization of the Erdős-Sierpiński conjecture

Amirali Fatehizadeh

In this paper, we investigate the combinatorial structure and asymptotic distribution of the solution set of the equation $σ (n + 1) = k σ (n)$ for a given integer $k > 1$ . From a combina…

math.NT2026

On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number Field

Amirali Fatehizadeh

In this article, we investigate the statistical distribution and asymptotic behavior of the family of monic integer polynomials of degree $n$ having at least one root in a fixed nu…

Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds

On the Divisibility Relation σ(n)∣σ(n+h) and a Generalized Erdős--Sierpiński Conjecture

A generalization of the Erdős-Sierpiński conjecture

On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number Field

On the Divisibility Relation $σ (n) ∣ σ (n + h)$ and a Generalized Erdős--Sierpiński Conjecture