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homework-05

# homework-05 - Problems in Part A will be marked by the...

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Modern Algebra and Geometry I Math 4000/6000 (92-321) Homework Assignments 5A and 5B – Due Friday, February 3 Homework is due at the start of class. Work that is not turned in at the beginning of class is considered late, and will not generally be accepted. Write your solutions in complete mathematical sentences. Always provide a complete justiﬁcation for each solution, even if a problem does not explicitly ask you to do so. When using a result from the textbook as part of a solution, clearly identify the result you are using, e.g., “. . . so the statement is true for all n N by the Principle of Mathematical Induction,” or “. . . and 34 7 34 (mod 7) by Proposition 3.3 of Chapter 1.” This assignment consists of two parts that must be turned in separately.
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Unformatted text preview: Problems in Part A will be marked by the course grader. Problems in Part B will be marked by the instructor. (A) 1. Â§ 1.3 # 8 (You should not have to compute any larger powers. Use modular arithmetic and simplify as you go along. You can use negative integers if it will simplify the computation.) 2. Â§ 1.3 # 10 3. Â§ 1.3 # 11 (use part (a) to do part (b)) 4. Â§ 1.3 # 16 5. Â§ 1.3 # 17 6. Â§ 1.3 # 20cg (Be sure to show all of your work.) (B) 1. Â§ 1.3 # 25 2. Â§ 1.3 # 29 3. Challenge problem: Formulate and prove the generalization of Â§ 1.1 #2. Additional practice problems: Â§ 1.3 # 1, 2, 5, 6, 7, 9, 12, 13, 15, 18, 19, 27, 28 These problems will not be collected, but cover material that you will be responsible for knowing. 1...
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