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Article

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

Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
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Mathematics 2020, 8(10), 1775; https://doi.org/10.3390/math8101775
Received: 5 September 2020 / Revised: 6 October 2020 / Accepted: 7 October 2020 / Published: 14 October 2020
(This article belongs to the Special Issue Algebra and Number Theory)
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. View Full-Text
Keywords: Diophantine equations; Prouhet Tarry Escott problem; Fibonacci pattern Diophantine equations; Prouhet Tarry Escott problem; Fibonacci pattern
MDPI and ACS Style

Raghavendran, S.; Narayanan, V. Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem. Mathematics 2020, 8, 1775. https://doi.org/10.3390/math8101775

AMA Style

Raghavendran S, Narayanan V. Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem. Mathematics. 2020; 8(10):1775. https://doi.org/10.3390/math8101775

Chicago/Turabian Style

Raghavendran, Srikanth, and Veena Narayanan. 2020. "Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem" Mathematics 8, no. 10: 1775. https://doi.org/10.3390/math8101775

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