Number Theory


A New Binomial Formula for the Sum of Two Powers

Authors: Julian Beauchamp

In this paper, we reveal a new binomial formula that expresses the sum of, or difference between two powers, a^x \pm b^y, as a binomial expansion of a single power, z. Like the standard binomial formula it includes the normal binomial coefficients, factors and indices, but includes an additional non-standard factor. The new formula (with an upper index z) mimics a standard binomial formula (to the power z) without the value of the binomial expansion changing even when z itself changes. This has exciting implications for certain diophantine equations. This short paper simply highlights its existence.

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Submission history

[v1] 2017-12-31 06:29:29

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