MathDB
Log area.

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November 27, 2005
logarithmsgeometryfloor functioninequalitiesrectanglenumber theoryrelatively prime

Problem Statement

Let SS be the set of ordered pairs (x,y)(x, y) such that 0<x≤10<x\le 1, 0<y≤10<y\le 1, and [log⁡2(1x)]\left[\log_2{\left(\frac 1x\right)}\right] and [log⁡5(1y)]\left[\log_5{\left(\frac 1y\right)}\right] are both even. Given that the area of the graph of SS is m/nm/n, where mm and nn are relatively prime positive integers, find m+nm+n. The notation [z][z] denotes the greatest integer that is less than or equal to zz.
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