#### Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 1-7.

### SQUARE EULERIAN QUADRUPLES

### Allan J. MacLeod

Mathematics and Statistics Group, University of the West of Scotland,
High St., Paisley, Scotland, PA1 2BE, UK

*e-mail:* `allan.macleod@uws.ac.uk`

**Abstract.** We consider the problem of finding four different rational
squares, such that the product of any two plus the sum of the same two
always gives a square. We give some historical background to this problem
and exhibit the small number of solutions found so far.

**2010 Mathematics Subject Classification.**
11A99, 11D09, 11G05, 11Y50.

**Key words and phrases.** Squares, Eulerian quadruples, elliptic curves.

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

**References:**

- L. E. Dickson, History of the Theory of Numbers, Vol. 2 Diophantine Analysis, AMS,
Chelsea, New York, 1992.

MathSciNet

- A. Dujella,
*An extension of an old problem of Diophantus and Euler*,
Fibonacci Quarterly **37** (1999), 312-314.

MathSciNet

- A. Dujella,
*An extension of an old problem of Diophantus and Euler. II*,
Fibonacci Quarterly **40** (2002), 118-123.

MathSciNet

- L. J. Mordell, Diophantine Equations, Academic Press, New York, 1968.

MathSciNet

*Rad HAZU* Home Page