Sums of squares, cubes, and higher powers

Jagy, William C.; Kaplansky, Irving

Experiment. Math., Tome 4 (1995) no. 4, p. 169-173 / Harvested from Project Euclid

Résumé

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.

Publié le : 1995-05-14
Classification: 11P05

@article{1062621075,
     author = {Jagy, William C. and Kaplansky, Irving},
     title = {Sums of squares, cubes, and higher powers},
     journal = {Experiment. Math.},
     volume = {4},
     number = {4},
     year = {1995},
     pages = { 169-173},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1062621075}
}

Jagy, William C.; Kaplansky, Irving. Sums of squares, cubes, and higher powers. Experiment. Math., Tome 4 (1995) no. 4, pp.  169-173. http://gdmltest.u-ga.fr/item/1062621075/