test3a.pdf - 1 Compute the following quantities Your answer to each part should be a number(a(−61 mod 7(b(−61 div 7 (c(−43)27 87 � 103 mod 11 (d

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1. Compute the following quantities. Your answer to each part should be a number. (a) ( - 61) mod 7 (b) ( - 61) div 7 (c) ( ( - 43) 27 + 87 · 103 ) mod 11 (d) ( 28 - (38 + 11) 231 ) mod 6 2. Here are two prime factorizations: 30345 = 3 · 5 · 7 · 17 2 and 442170 = 2 · 3 2 · 5 · 17 3 . Use this information to compute the prime factorization for each of the following numbers: (a) gcd(30345 , 442170) (b) lcm(30345 , 442170) (c) 30345 · 442170 3. Group the following numbers into equivalence classes mod 12. That is, put two numbers in the same group if and only if they are equivalent mod 12. {- 57 , - 30 , - 17 , - 14 , 58 , 60 , 82 , 96 , 114 , 118 , 123 , 132 } 4. Use Euclid’s algorithm to compute gcd(85 , 245). Show all the steps. You may represent the steps as a sequence of equations or as a sequence of rows in a table, but make sure that the grader can follow what you are doing. Note: the purpose of this question is to determine whether you understand Euclid’s algorithm, not whether you can answer this question by some other means. If we don’t see evidence that you

• Fall '07
• Jarecki

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