On the Polynomial Structure of 𝑟𝑘(𝑛)
R. Sivaraman1, J. López-Bonilla2, S. Vidal-Beltrán3
1Dr. R. Sivaraman, Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Chennai 600 106, Tamil Nadu, India.
2Prof. J. López-Bonilla, ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México.
3S. Vidal-Beltrán, ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP 07738, CDMX, México.
Manuscript received on 16 September 2023 | Revised Manuscript received on 02 October 2023 | Manuscript Accepted on 15 October 2023 | Manuscript published on 30 December 2023 | PP: 4-5 | Volume-3 Issue-2, October 2023 | Retrieval Number: 100.1/ijam.A1162044124 | DOI: 10.54105/ijam.A1162.103223
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: If 𝒓𝒌(𝒏) is the number of representations of a positive integer n as the sum of k squares, then 𝒓𝒌(𝒏) is a polynomial in k of degree n; here we exhibit expressions for certain coefficients through this polynomial.
Keywords: Sum of Divisors Function, Sequences of Integers, Sums of Squares, Recurrence Relations.
Scope of the Article: Number Theory