We answer the question: for any p, q ∈ R with p≠q and p≠ - q, what are the greatest value ? = ?(p, q) and the least value µ = µ(p, q), such that the double inequality M?(a, b) p(a, b)Mq(a, b) 0 with a≠b? Where Mp(a, b) is the pth power mean of two positive numbers a and b.
