(SI17-15) On Becker’s Conjecture

Authors

• Jitender ., Motilal Nehru National Institute of Technology Allahabad
• Shiv Datt Kumar, Motilal Nehru National Institute of Technology Allahabad

Abstract

In this paper, we explore identities that involve higher-degree versions of widely recognized composition formulae, specifically focusing on expressions of the form

(x^k₁ + x^k₂ + · · · + x^k_r ) · (y^k₁ + y^k₂ + · · · + y^k_s ) = (z^k₁ + z^k₂ + · · · + z^k_n),

where k ≥ 2, y = (y₁, y₂, . . . , y_s), x = (x₁, x₂, . . . , x_r), are indeterminates and all zi are linear form in y with coefficients belongs to the rational field F(x₁, x₂, . . . , x_r), over any field of characteristic zero. One key result is that if such an identity exists, then n ≥ 2s. This states a relationship between the number of terms on the right hand side and that involving y on the left hand side.

Recommended Citation

., Jitender and Kumar, Shiv Datt (2026). (SI17-15) On Becker’s Conjecture, Applications and Applied Mathematics: An International Journal (AAM), Vol. 21, Iss. 4, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol21/iss4/3