Jagy, William C.; Kaplansky, Irving Sums of squares, cubes, and higher powers. (English) Zbl 0867.11066 Exp. Math. 4, No. 3, 169-173 (1995). Some problems concerning representability of integers as \(x^{k_1}+y^{k_2}+z^{k_3}\) with \(1/k_1+1/k_2+ 1/k_3>1\) are investigated experimentally, discussing questions of positivity of the variables as well. Lists of exceptions (i.e., numbers not represented) are obtained in several cases. For the case of sums of two squares and a ninth power, an infinite series of exceptions is exhibited. Reviewer: R.Schulze-Pillot (Saarbrücken) Cited in 1 ReviewCited in 3 Documents MSC: 11P05 Waring’s problem and variants 11-04 Software, source code, etc. for problems pertaining to number theory Keywords:sums of powers; generalized Waring problem PDF BibTeX XML Cite \textit{W. C. Jagy} and \textit{I. Kaplansky}, Exp. Math. 4, No. 3, 169--173 (1995; Zbl 0867.11066) Full Text: DOI Euclid EuDML EMIS OpenURL Online Encyclopedia of Integer Sequences: Numbers that are not the sum of 2 squares and a nonnegative cube. Number of partitions of n into 2 squares and 2 nonnegative cubes. Numbers that are not the sum of 2 squares and a 4th power. Numbers of the form 216*p^3, where p is a Pythagorean prime (A002144). Numbers that are not the sum of {2 squares, a nonnegative cube, and a nonnegative k-th power with k >= 17}. a(n) = number of nonnegative integers that are not the sum of {2 squares, a nonnegative 5th power, and a nonnegative n-th power}. a(n) = largest number k that is not the sum of {2 squares, a nonnegative 5th power, and a nonnegative n-th power}. References: [1] Cohn J. H. E., J. London Math. Soc. 5 pp 74– (1972) · Zbl 0247.10028 [2] Davenport H., Proc. London Math. Soc. 43 pp 73– (1937) · Zbl 0016.24601 [3] Davenport H., Proc. London Math. Soc. 43 pp 142– (1937) · Zbl 0016.34806 [4] DOI: 10.1007/BF01234411 · Zbl 0692.10020 [5] Elkies N., Amer. Math. Monthly 102 pp 70– (1995) [6] Kevin Ford B., J. London Math. Soc. 51 pp 14– (1995) · Zbl 0816.11049 [7] Halberstam H., J. London Math. Soc. 25 pp 158– (1950) · Zbl 0037.31101 [8] Mordell L. J., Diophantine Equations (1969) · Zbl 0188.34503 [9] Roth K. F., J. London Math. Soc. 24 pp 4– (1949) · Zbl 0032.01401 [10] Vaughan R. C., The Hardy–Littlewood Method (1981) · Zbl 0455.10034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.