Experimental Mathematics

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.


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