Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem

Srikanth Raghavendran and Veena Narayanan
Additional contact information
Srikanth Raghavendran: Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
Veena Narayanan: Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India

Mathematics, 2020, vol. 8, issue 10, 1-18

Abstract: The present study aims to develop novel parametric solutions for the Prouhet Tarry Escott problem of second degree with sizes 3, 4 and 5. During this investigation, new parametric representations for integers as the sum of three, four and five perfect squares in two distinct ways are identified. Moreover, a new proof for the non-existence of solutions of ideal Prouhet Tarry Escott problem with degree 3 and size 2 is derived. The present work also derives a three parametric solution of ideal Prouhet Tarry Escott problem of degree three and size two. The present study also aimed to discuss the Fibonacci-like pattern in the solutions and finally obtained an upper bound for this new pattern.

Keywords: Diophantine equations; Prouhet Tarry Escott problem; Fibonacci pattern (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/10/1775/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/10/1775/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:10:p:1775-:d:427803

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().