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On some theorems in the theory of numbers

Published online by Cambridge University Press:  20 January 2009

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The number of groups of n which may be selected from 2n is 2n(2n − l)…(n + l)/n! But make the 2n into two groups of n, and select r out of the first and nr out of the second. This gives [n(n−l)…(nr+l)/r!] + [n(n−l)…(r + l)/(nr)!] ways of thus making a group of n. Hence

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1889

References

* The use of this identity was suggested to me by Professor Tait.

* Compare a paper by MrLeudesdorf, , in the Proceedings of the Lond. Math. Soc. for 1889, p. 199–a paper which I did not see till after the above was written.Google Scholar