Valery Asiryan

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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.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…