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Unformatted text preview: x 3 + 3 xy + y 3 = 1 contains only one set of three distinct points A , B and C which are the vertices of an equilateral triangle, and nd its area. [Putnam Exam, 2006, B1] Problem 5. Dene a function f on the real numbers by f ( x ) = ( if x is irrational, 1 /q if x = p/q with p Z ,q N , gcd( p,q ) = 1 . Determine the set of points on which f is continuous. Problem 6. Dene a sequence { u n } n =0 by u = u 1 = u 2 = 1, and thereafter by the condition that det u n u n +1 u n +2 u n +3 = n ! for all n 0. Show that u n is an integer for all n . (By convention, 0! = 1.) [Putnam Exam, 2004, A3]...
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This note was uploaded on 02/29/2012 for the course MATH 1190 taught by Professor Ryandaileda during the Fall '10 term at Trinity University.
 Fall '10
 RyanDaileda
 Real Numbers

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