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ALGEBRAIC CURVES W4045 1. Homework, week 1, due September 15 1. (Linear diophantine equations) Let a, b, c ∈ Z. Give necessary and sufficient conditions for the existence of a solution to the diophantine equation ax + by = c with x, y ∈ Z. 2. Exercises 1.1, 1.2, and 1.3 in the Miles Reid book. 1