For any we establish inequalities between the two homogeneous polynomials and in the positive orthant Conditions for yield a new proof and broad generalization of the number theoretic inequality that for base the sum of all nonempty products of digits of any never exceeds and equality holds exactly when all auxiliary digits are Links with an inequality of Bernoulli are also noted. When and is strictly positive, the surface lies between the planes and For fixed we explicitly determine functions of such that this surface is as and as
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