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Unformatted text preview: integers m 1 ,m 2 ,m 3 ,m 4 ,m 5 such that the polynomial p ( x ) = ( xm 1 )( xm 2 )( xm 3 )( xm 4 )( xm 5 ) has exactly k nonzero coecients. 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 c is the greatest integer less than or equal to .) [Putnam Exam, 2005, B1]...
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 Fall '10
 RyanDaileda
 Derivative

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