Modern Algebra and Geometry I Math 4000/6000 (92-321) Homework Assignments 6A and 6B – Due Friday, February 10 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. § 1.3 # 21b. Determine all possible solutions to the pair of congruence equations. (Show all of your work. Do not merely invoke the formulas in the textbook. No guess and check.)
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