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Equal Sums of Like Powers

Published online by Cambridge University Press:  20 November 2018

E. M. Wright*
Affiliation:
University of Aberdeen
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In what follows small latin letters denote rational integers (whole numbers) and we write

Let us consider the system of k equations

1

that is

These equations are obviously satisfied if the b are a permutation of the a; such a solution we call trivial.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bastien, L., Sphinx-Oedipe 8(1913), 171-172.Google Scholar
2. Dickson, L. E., History of the Theory of Numbers, vol.2, Washington, 1920, Ch. 24.Google Scholar
3. Gloden, A., Mehrgradige Gleichungen, Groningen, 1944.Google Scholar
4. Hardy, G.H. and Wright, E. M., Introduction to the Theory of Numbers, 4th ed. (Oxford 1960), 328-32.Google Scholar
5. Hua, L. K., Quart. J. of Math. 9(1938), 315-20.Google Scholar
6. Hunter, W., Journ. London Math. Soc. 16(1941), 177-9.Google Scholar
7. Lehmer, D. H., The Tarry-Escott problem, Scripta Math. 13(1947), 37-41.Google Scholar
8. Prouhet, E., Acad, C. R., Sci. (Paris) 33(1851), 225.Google Scholar
9. Wright, E. M., Equal sums of like powers, Proc, Edinburgh Math. Soc. 8(1949), 138-42.Google Scholar
10. Wright, E. M., Prouhet' s 1851 solution of the Tarry-Escott problem of 1910, Amer. Math. Monthly 66(1959), 199-201.Google Scholar
11. Wright, E. M., An easier Waring' s problem, Journ. London Math. Soc. 9(1934), 267-72.Google Scholar