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Unformatted text preview: c , then ab  c . 6. A positive integer n is called a per±ect square i± n = m 2 ±or some integer m . (a) Prove that the positive integer n is a per±ect square i± and only i± when we ±actor it into a product o± powers o± distinct primes n = p k 1 1 p k 2 2 · · · p k ℓ ℓ all o± the k i are even. (b) Suppose that a, b, c ∈ P , with gcd( a, b ) = 1 and ab = c 2 . Prove that a and b are per±ect squares. 7. (a) What is the remainder when 8 20 is divided by 3? (b) Is 6 17 + 17 6 divisible by 3 or 7? 8. Which o± the ±ollowing integers are congruent modulo 6?147 ,91 ,22 ,14 , 2 , 4 , 5 , 21 , 185. Recommended Problems 1. Text, page 50 #42. 2. Text, page 51 #44. 3. Text, page 52 #75. 4. Text, page 52 #79. 5. Text, page 54 #92. 6. Prove that if a  b , then a 2  b 2 . 7. Prove that if a 2  b 2 , then a  b . 8. Text page 84 #56. 9. Text page 84 #57....
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This note was uploaded on 02/05/2009 for the course MATH 101 taught by Professor Johnson during the Spring '08 term at Adelphi.
 Spring '08
 JOHNSON
 Linear Algebra, Algebra

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