## Experimental Mathematics

- Experiment. Math.
- Volume 4, Issue 3 (1995), 169-173.

### Sums of squares, cubes, and higher powers

William C. Jagy and Irving Kaplansky

#### Abstract

Any integer is expressible as a sum of two squares and a cube, mixed signs being allowed. We study the analogous question for a square and two cubes, and obtain an affirmative answer in the range from $-$4,000,000 to 2,000,000. For two squares and a cube with everything positive, computations support the possibility that there are only finitely many exceptions. However, $x^2 + y^2 + z^9$ admits infinitely many positive exceptions.

#### Article information

**Source**

Experiment. Math., Volume 4, Issue 3 (1995), 169-173.

**Dates**

First available in Project Euclid: 3 September 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1062621075

**Mathematical Reviews number (MathSciNet)**

MR1387474

**Zentralblatt MATH identifier**

0867.11066

**Subjects**

Primary: 11P05: Waring's problem and variants

#### Citation

Jagy, William C.; Kaplansky, Irving. Sums of squares, cubes, and higher powers. Experiment. Math. 4 (1995), no. 3, 169--173. https://projecteuclid.org/euclid.em/1062621075