MathDB
P 12

Source:

May 25, 2007
functionfloor functioninequalitieslogarithmscalculusintegrationarticles

Problem Statement

The positive function p(n)p(n) is defined as the number of ways that the positive integer nn can be written as a sum of positive integers. Show that, for all positive integers n≥2n \ge 2, 2⌊n⌋<p(n)<n3⌊n⌋.2^{\lfloor \sqrt{n}\rfloor}< p(n) < n^{3 \lfloor\sqrt{n}\rfloor }.
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