Unformatted text preview: integers m 1 ,m 2 ,m 3 ,m 4 ,m 5 such that the polynomial p ( x ) = ( x-m 1 )( x-m 2 )( x-m 3 )( x-m 4 )( x-m 5 ) has exactly k nonzero coeﬃcients. Find, with proof, a set of integers m 1 ,m 2 ,m 3 ,m 4 ,m 5 for which this minimum k is achieved. [Putnam Exam, 1985, B1] Problem 5. Find a nonzero polynomial P ( x,y ) such that P ( b a c , b 2 a c ) = 0 for all real numbers a . ( Note: b ν c is the greatest integer less than or equal to ν .) [Putnam Exam, 2005, B1]...
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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