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Two More Tripos Questions

Published online by Cambridge University Press:  03 November 2016

G.N. Watson
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Extract

The following problem was included in the paper set in the Mathematical Tripos on the morning of January 5, 1881 :

iii. Prove that, if a + b + c = 0 and x + y + z = 0, then 4(ax + by + cz)3 - 3(ax+ by + cz)( a2+ b2+ c2)(a2+ y2 + z2) - 2 (b - c) (c - a) (a - b)(y - z) (z - x) (z - y)=54abcxyz.

A solution of this problem was published by A. Cayley in June 1881 ; see the Messenger of Mathematics, XI. (1882), 23-25. Cayley's solution took the form of a long and cumbrous verification, and he admitted that he did not know the origin of the result nor did he see any simple way of proving it.

Type
Research Article
Information
The Mathematical Gazette , Volume 39 , Issue 330 , December 1955 , pp. 280 - 286
Copyright
Copyright © The Mathematical Association 1955

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References

* Hansard quotes Dr. Hill as saying : “ The reply to my hon. friend is that pH is the negative of the logarithm of the hydrogen ion concentration measured in grams per litre of solution.”—The Times, January 28th, 1954.