Valery Asiryan

collaborators

9 papers

math.GM2026

On the Rank Condition for Perfect Cuboids

Valery Asiryan

Paulsen and West associate perfect cuboids with triples of rational points on a congruent-number elliptic curve and assert that the corresponding curve has rank at least two. The p…

math.GM2026

Finiteness in Square Classes and Weighted Zero Density of Perfect Cuboids

Valery Asiryan

Let $M (N)$ be the number of similarity classes of positive rational perfect cuboids with ordered edges $a, b, c$ , space diagonal $g$ , and squarefree invariant $N=\operatorname{sf}(ab…

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…

math.NT2025

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.GM2025

On the Irreducibility of the Cuboid Polynomial $P_{a, u} (t)$

Valery Asiryan

In this paper we consider the even monic degree-8 cuboid polynomial $P_{a, u} (t)$ with coprime integers $a \neq = u > 0$ . We prove irreducibility over $Z$ by excluding all degre…

math.GM2025

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…

On the Rank Condition for Perfect Cuboids

Finiteness in Square Classes and Weighted Zero Density of Perfect Cuboids

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

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

On the Irreducibility of the Cuboid Polynomial Pa,u​(t)

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

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

On the Irreducibility of the Cuboid Polynomial $P_{a, u} (t)$

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