MathDB
Putnam 2004 B3

Source:

December 11, 2004
Putnamfunctiongeometryperimetercollege contests

Problem Statement

Determine all real numbers a>0a>0 for which there exists a nonnegative continuous function f(x)f(x) defined on [0,a][0,a] with the property that the region R={(x,y):0≤x≤a,0≤y≤f(x)}R=\{(x,y): 0\le x\le a, 0\le y\le f(x)\} has perimeter kk units and area kk square units for some real number kk.
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