Valery Asiryan

collaborators

7 papers

math.NT2026

Genus-One Fibrations and the Jacobian of Linear Slices in the Quintic Equal-Sum Problem

Valery Asiryan

We study the Diophantine equation $a^{5} + b^{5} = c^{5} + d^{5}$ under the linear slicing constraint $(c + d) - (a + b) = h$ . We first prove the necessary congruence $30 ∣ h$ . After symmetrization, t…

math.GM2026

Irreducibility of the Cuboid Polynomial $P_{a, u} (t)$ via a Rank-Zero Elliptic Curve

Valery Asiryan

In this paper we study the even monic degree-8 cuboid polynomial $P_{a, u} (t)$ introduced by R.A. Sharipov in the first-cuboid specialization of his cuboid equations. For nonzero in…

math.GM2026

Computational Evidence Against Quadratic-Cubic Factorization for the Second Cuboid Quintic

Valery Asiryan, Randall L. Rathbun

Let $Q_{p, q} (t) \in Z [t]$ be Sharipov's even monic degree- $10$ second cuboid polynomial depending on coprime integers $p \neq = q > 0$ . Writing $Q_{p, q} (t)$ as a quintic in $t^{2…

math.GM2026

Non-Existence of Linear-Quartic Factorization for the Second Cuboid Quintic

Valery Asiryan

Let $Q_{p, q} (t) \in Z [t]$ be Sharipov's even monic degree- $10$ second cuboid polynomial depending on coprime integers $p \neq = q > 0$ . Writing $Q_{p, q} (t)$ as a quintic in $t^{2…

math.GM2026

Non-Existence of Quintic Factorization for the Second Cuboid Polynomial $Q_{p, q} (t)$

Valery Asiryan

We consider the even monic degree- $10$ second cuboid polynomial $Q_{p, q} (t) \in Z [t]$ depending on coprime integers $p \neq = q > 0$ . We exclude the existence of a splitting of t…

math.NT2025

The Linear Slicing Method for Equal Sums of Like Powers: Modular and Geometric Constraints

Valery Asiryan

We study the Diophantine equation $a^{k} + b^{k} = c^{k} + d^{k}$ with integer variables and exponent $k > 1$ , under the linear constraint $(c + d) - (a + b) = h$ . We analyze the geometry and ar…

Genus-One Fibrations and the Jacobian of Linear Slices in the Quintic Equal-Sum Problem

Irreducibility of the Cuboid Polynomial Pa,u​(t) via a Rank-Zero Elliptic Curve

Computational Evidence Against Quadratic-Cubic Factorization for the Second Cuboid Quintic

Non-Existence of Linear-Quartic Factorization for the Second Cuboid Quintic

Non-Existence of Quintic Factorization for the Second Cuboid Polynomial Qp,q​(t)

The Linear Slicing Method for Equal Sums of Like Powers: Modular and Geometric Constraints

Irreducibility of the Cuboid Polynomial $P_{a, u} (t)$ via a Rank-Zero Elliptic Curve

Non-Existence of Quintic Factorization for the Second Cuboid Polynomial $Q_{p, q} (t)$