homework-07 - Modern Algebra and Geometry I Math...

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Unformatted text preview: Modern Algebra and Geometry I Math 4000/6000 (92-321) Homework Assignment 7A – Due Monday, February 20 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. Problems in Part A will be marked by the course grader. Problems in Part B will be marked by the instructor. (A) 1. § 1.4 # 7 2. § 1.4 # 12 3. (a) Compute 26- 1 in Z 105 , or else explain why it does not exist. (No guess and check.), or else explain why it does not exist....
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