논문KCI 등재
On the Tarry-Escott and Related Problems for 2 × 2 matrices over Q
경북대학교 자연과학대학 수학과|2023.09|Kyungpook Mathematical Journal|제63권 제3호|pp. 345-353|DOI 10.5666/KMJ.2023.63.3.345
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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)
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)
참고문헌 (6)
- A. Alpers, "The two-dimensional Prouhet-Tarry-Escott problem", J. Number Theory, 123(2), pp.403~412 (2007)
- P. Borwein, "The Prouhet-Tarry-Escott problem revisited", Enseign. Math, 40(2), pp.3~27 (1994)
- A. Choudhry, "Matrix analogues of the Tarry-Escott problem, multigrade chains and the equation of Fermat", Math. Student, 75, pp.215~224 (2006)
- B. Cohen, "Generalized Pell Equation for 2 × 2 matrices", Discuss. Math. GAA, 37, pp.13~30 (2017)
- H. L. Dorwart, "The Tarry-Escott Problem", Amer. Math. Monthly, 44(10), pp.613~626 (1937)
- L. N. Vaserstein, "Noncommutative number theory, in Algebraic K-theory and Algebraic Number Theory", Contemp. Math, 83, pp.445~449 (1989)
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