Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 55-64.
SMALL-DEGREE PARAMETRIC SOLUTIONS FOR DEGREE 6 AND 7 IDEAL MULTIGRADES
Allan J. Macleod
Statistics, O.R. and Mathematics Group (Retired),
University of the West of Scotland, High St., Paisley, Scotland. PA1 2BE
e-mail: peediejenn@hotmail.com
Abstract. We derive parametric solutions for 6 and 7 term ideal
multigrades. These are of significantly smaller degree than previous solutions,
such as those of Chernick.
2020 Mathematics Subject Classification.
11D25, 11P05, 11Y50.
Key words and phrases. Multigrade, parametric solution, elliptic curve.
Full text (PDF) (free access)
DOI: https://doi.org/10.21857/yvjrdcvrwy
References:
- J. Chernick, Ideal solutions of the Tarry-Escott problem, Amer. Math. Monthly 44
(1937), 626-633.
MathSciNet
CrossRef
- A. Choudhry, A new approach to the Tarry-Escott problem, Int. J. Number Theory 13
(2017), 393-417.
MathSciNet
CrossRef
- A. Gloden, Mehrgradige Gleichungen, Noordhoff, Groningen, 1944.
MathSciNet
- A. J. MacLeod, On Crussol's method for Σi=14 Xin
= Σi=14 Yin, n=2,4,6,
Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 20 (2016), 19-26.
MathSciNet
- L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
MathSciNet
- T. Piezas III, A Collection of Algebraic Identities, website available at
https://sites.google.com/site/tpiezas/Home.
- C. Shuwen, Equal Sums of Like Powers, website available at
http://eslpower.org/eslp.htm.
- C. J. Smyth, Ideal 9th-order multigrades and Letac's elliptic curve,
Math. Comp. 57 (1991), 817-823.
MathSciNet
CrossRef
Rad HAZU Home Page