Euler's and the Taxi Cab relations and other numbers that can be written twice as sums of two cubed integers

2022/05/29 by Vladimir Pletser, Pletser, Vladimir
Mathematics · #11D25 (Primary) 11B37 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B37 #msc:11D25

paper · pdf · doi:10.48550/arxiv.2206.00465

7 pages, 1 figure

arxiv created 2022/05/29 · arxiv updated 2022/06/02

Abstract

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.

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