#### Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 19-26.

### ON CRUSSOL’S METHOD FOR Σ_{i=1}^{4} *X*_{i}^{n}
= Σ_{i=1}^{4} *Y*_{i}^{n}, *n*=2,4,6

### Allan J. MacLeod

Statistics, O.R. and Mathematics Group (retired), University of the West of Scotland,
High St., Paisley, Scotland. PA1 2BE, UK

*e-mail:* `peediejenn@hotmail.com`

**Abstract.** Crussol gave a method for computing non-trivial integer
solutions to the equations in the title. We show that the method can be
linked to finding points on either of two possible elliptic curves, both of
which have rank greater than zero.

**2010 Mathematics Subject Classification.**
11D09, 11Y50.

**Key words and phrases.** Elliptic curve, Crussol, multigrade.

**Full text (PDF)** (free access)

**References:**

- L. E. Dickson, History of the Theory of Numbers, Volume II, Diophantine Analysis,
AMS Publishing, New York, 1992.

MathSciNet

- A. Gloden,
*Aperçu historique des multigrades*, Bull. Soc. Nat. Luxemb. **54** (1950) 5-17.

MathSciNet

- L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.

MathSciNet

- J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer-Verlag,
New York, 1992.

MathSciNet
CrossRef

- D. Simon,
*Computing the rank of elliptic curves over number fields*, LMS J. Comput. Math. **5** (2002)
7-17.

MathSciNet
CrossRef

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