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Relations Between the Digits of Numbers and Equal Sums of Like Powers

Published online by Cambridge University Press:  20 November 2018

J. B. Roberts
J. B. Roberts*
Affiliation:
University of London and Reed College
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I t is straightforward, but tedious, to write down the integers whose representations in a given base do not have particular digits in certain positions. In the first section of this paper we give a computational scheme that enables us to carry out such operations in a rapid and simple fashion.

In the second section of the paper we derive a general identity involving the digits of integers in arbitrary Cantor systems of notation.

In the third section we apply this identity and deduce a number of results concerned with the splitting of integers into classes with equal power sums. The computational scheme of the first section leads us to an algorithm for the determination of such splittings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 626 - 636
Copyright
Copyright © Canadian Mathematical Society 1964

References

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