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Math 366 HW 1, Spring 2014 This assignment is due Friday, January 31 in class. Feel free to work together, but be sure to write up your own solutions. As for writing it up, please write legibly on your own paper, including as much justification as seems necessary to get the point across (little for 1–4, much for 5). 1. For n = 5, 8, 12, and 17, find all positive integers less than n and relatively prime to n. 2. Determine gcd(23 · 3 · 5 · 7 · 13, 22 · 33 · 7 · 11). 3. Determine the least common multiple of the same two numbers. 4. Find integers s and t so that 1 = 5s + 13t and show that these choices are not unique. 5. For positive integers a and b, show that a · b = gcd(a, b) · lcm(a, b). NOTE: This assignment is pretty short as we got off to a slow start. You can expect as many as 10 problems on usual assignments. 1