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Unformatted text preview: every subset of 3 attendees spoke a common language. Prove that some language was spoken by at least 200 of the people at the meeting. 3. Prove that there exist integers a, b, c , not all zero and each of absolute value less than one million, such that  a + b 2 + c 3  < 1011 . 4. Given two relatively prime positive integers a, b and an integer m ( a1)( b1), prove that there exist nonnegative integers x, y such that m = ax + by . 5. A set S of integers is called sumfree if there do not exist x, y, z S with x + y = z . What is the maximum size of a sumfree subset of { 1 , 2 , 3 , . . . , 2 n + 1 } ? 6. Let B be a set of more than 2 n +1 n distinct points with coordinates of the form ( 1 , 1 , . . . , 1) in R n , with n 3. Show that there are three distinct points in B which are the vertices of an equilateral triangle. 2...
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This note was uploaded on 03/13/2010 for the course MATH 4801 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Staff
 Math

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