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A double partition problem asks for a number of nonnegative integer solutionsto a system of two linear Diophantine equations with integer coefficients.Artur Cayley suggested a reduction of a double partition to a sum of scalarpartitions with an algorithm subject to a set of conditions. We show that whenthese conditions are not satisfied and the original algorithm fails itsmodification solves the reduction problem.

On Cayley algorithm for double partition