MATH 4200 Midterm: MATH 4200 LSU Fall 18 Exam 1a
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Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. There is a total of 70 points possible. Put your name on each page of your paper: [12 points] let m = 143 and n = 176. (a) calculate the greatest common divisor d = gcd(m, n). Therefore, d = gcd(143, 176) = 11. (b) write d in the form sm + tn for some integers s and t. = 143 4(176 1 143) = 5 143 4 176: [12 points] use induction to prove one of the following. Take your pick. (just make a direct induction proof. Do not assume any other facts about congruences or summation formulas. ) (a) for any positive integer n, n3 + 5n is a multiple of 3. Let s(n) be the statement: n3 + 5n is a multiple of 3 for the integer n.
