Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Tarry-Escott and Related Problems for 2 × 2 matrices over ℚ

  • Supawadee Prugsapitak (Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University) ;
  • Walisa Intarapak (Algebra and Applications Research Unit, Division of Computational Science, Faculty of Science, Prince of Songkla University) ;
  • Vichian Laohakosol (Department of Mathematics, Faculty of Science, Kasetsart University)
  • Received : 2022.10.31
  • Accepted : 2023.07.05
  • Published : 2023.09.30
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Abstract

Reduced solutions of size 2 and degree n of the Tarry-Escott problem over M2(ℚ) are determined. As an application, the diophantine equation αAn + βBn = αCn + βDn, where α, β are rational numbers satisfying α + β ≠ 0 and n ∈ {1, 2}, is completely solved for A, B, C, D ∈ M2(ℚ).

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Acknowledgement

We would like to express our gratitude to the referee(s) for comments and suggestions.

References

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