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This note records a curious numerical identity: the number 1318, connectedwith Vandermonde's cyclotomic quintic, may be decomposed in two distinct waysas 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 ofAbelian and generalized Abelian equations, we conjecture the existence of aninfinite number of analogous decompositions, involving arbitrarily large setsof numbers.

Vandermonde's quintic and multiple decompositions of the number 1318