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Some Proofs of Newton's Theorem on Sums of Powers of Roots

Published online by Cambridge University Press:  20 January 2009

R. F. Muirhead
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This well-known theorem, published in Newton's Arithmetica Universalis, may be formulized thus:—

where sm ≡ the sum of the mth powers of the roots of the equation

Of course, when m>n, certain coefficients pn+1, pn+2, … pm will be zero, and the last term that does not vanish will be .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , February 1904 , pp. 66 - 70
Copyright
Copyright © Edinburgh Mathematical Society 1904