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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Srikanth Raghavendran & Veena Narayanan, 2020. "Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1775-:d:427803
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    Cited by:

    1. Petr Karlovsky, 2021. "Diophantine Equations Relating Sums and Products of Positive Integers: Computation-Aided Study of Parametric Solutions, Bounds, and Distinct-Term Solutions," Mathematics, MDPI, vol. 9(21), pages 1-18, November.

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