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Unformatted text preview: Numbers & Polys MAS3300 Exam-C Prof. JLF King 4Jun2008 Note. This is an open brain, open ( pristine ) Sigmon- Notes exam. Please write each solution on a separate sheet of paper. Please be sure to write expressions unam- biguously e.g, the expression “1 /a + b ” should be bracketed either [1 /a ]+ b or 1 / [ a + b ]. Be careful with negative signs! Each question is an essay question unless specified oth- erwise. C1: Show no work; no partial credit. a Let Γ := Gcd(165 , 63) and find particular num- bers so that 165 A + 63 B = Γ. Then Γ= , A = , B = . b Note that Gcd(165 , 63 , 7) = 1. Find particular numbers C,D,E so that 165 C + 63 D + 7 E = 1: C = , D = , E = . [ Hint: Gcd ( Gcd(165 , 63) , 7 ) = 1.] c Let I comprise the irrational numbers and let A be the set of algebraic numbers. In terms of cardinality, then, I ? A where relation “?” is: ↔ ≺ (Circle the correct relation.) C2: Define a “tribonacci” sequence b by: b 1 := 1, b 2 := 2, b 3 := 3 and, for each n > 4, b...
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This note was uploaded on 01/26/2012 for the course MAS 3300 taught by Professor Staff during the Summer '08 term at University of Florida.
- Summer '08