Vandermonde's quintic and multiple decompositions of the number 1318

Jason A. C. Gallas

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arXiv · 0812.4850

Vandermonde's quintic and multiple decompositions of the number 1318

Jason A. C. Gallas

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Abstract

This note records a curious numerical identity: the number 1318, connected with Vandermonde's cyclotomic quintic, may be decomposed in two distinct ways as a sum of products of pairs of numbers taken from the set \{$6, 16, 26, 41$\}, namely $1318 = 6\cdot41 + 16\cdot26 + 16\cdot41 = 6\cdot16 + 6\cdot26 + 26\cdot41$. Based on the existence of radical solutions of certain families of Abelian and generalized Abelian equations, we conjecture the existence of an infinite number of analogous decompositions, involving arbitrarily large sets of numbers.

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Jason A. C. Gallas. 2008-12-28. Vandermonde's quintic and multiple decompositions of the number 1318. https://arxiv.org/abs/0812.4850

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