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The continued search for sums of powers

Published online by Cambridge University Press:  14 February 2019

Nigel Derby
Nigel Derby*
Affiliation:
36 Aylward Gardens, Chesham HP5 2QY e-mail: nderby2001@gmail.com
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Extract

In a previous paper [1], I described a method for computing sums of powers via a matrix composed from Pascal's triangle. (The motivation for this came from a mathematical puzzle posed by Paul Maslanka in the Guardian.) Since then I have read or viewed a number of papers on sums of powers. Some were nearly four hundred years old and the most recent one was published this year. One rather obscure work I stumbled across was ‘On the sums of powers of natural numbers’ by the Japanese mathematician Mr T. Kariya, published in Tokyo in 1907. If any readers know more of Mr Kariya I would be glad to hear about him.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 556 , March 2019 , pp. 94 - 100
Copyright
Copyright © Mathematical Association 2019 

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References

1. Derby, Nigel, The search for sums of powers, Math. Gaz. 99 (November 2015) pp. 416–421.10.1017/mag.2015.77Google Scholar
2. Gauss, C. F. and Schumacher, H. C., Correspondence between C. F Gauss and H. C. Schumacher, Ed. C. A. F. Peters (1861) available at htpps://archive.org/details/briefwechselzwi02schugoog/page/n9Google Scholar
3. Kariya, T., On the sums of powers of natural numbers (1907) in Mathematical papers from the Far East, Ed. Yoshio Mikami, Leipzig, B. G. Teubner (1910).Google Scholar
4. Pietrocola, Giorgio, On polynomials for the calculation of sums of powers of successive integers and Bernoulli numbers deduced from the Pascal's triangle, his web-site www.pietrocola.eu (June 2017).Google Scholar