Euler’s and the taxi cab relations and other numbers that can be written twice as sums of two cubed integers

We show that Euler’s relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the...

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Bibliographic Details
Published in:Open Journal of Mathematical Sciences 2024-12, Vol.8 (1), p.26-31
Main Author: PLETSER, Vladimir
Format: Article
Language:English
Online Access:Get full text
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Summary:We show that Euler’s relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two families. Their recursive and parametric equations are calculated.
ISSN:2616-4906
2523-0212
DOI:10.30538/oms2024.0222