final-spring97 - Name: MAS 3300 Numbers and Polynomials...

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Unformatted text preview: Name: MAS 3300 Numbers and Polynomials Spring 1997 FINAL EXAM Instructions: There are 12 questions. Do only TEN questions. With TEN complete problems there are 100 total points. Write on ONE side of the paper provided. Show all necessary working and reasoning to receive full credit. Your work needs to be written in a proper and coherent fashion. When giving proofs your reasoning should be clear. Calculators are allowed. You may answer questions 4(ii), and 12(i) on the Test Paper. A table of primes is supplied. PLEASE GRADE THE FOLLOWING TEN QUESTIONS: 1 1. [10 points] Let a R . Prove a 0 = 0 . 2. [10 points] Let a , b R and suppose a < 0 and b < 0. Prove ab > . 3. [10 points] Use mathematical induction to prove 1 2 + 2 2 + 3 2 + + n 2 = 1 6 n ( n + 1)(2 n + 1) , for all integers n 1. 4. [1 + 1 + 8 = 10 points] (i) Define what it means for two integers to be relatively prime ....
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This note was uploaded on 06/03/2011 for the course MAS 3300 taught by Professor Staff during the Spring '08 term at University of Florida.

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final-spring97 - Name: MAS 3300 Numbers and Polynomials...

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