MATH 4023 Midterm: MATH 4023 LSU 4023s04 Exam 1
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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. Put your name on each page of your paper: [18 points] prove by induction that for all positive integers n, n. X i=1 i(i 1) = (n 1)n(n + 1) 3: [16 points] (a) compute the greatest common divisor d = (1776, 1492) of the integers 1776 and. 1 = 13 101 41 32. All answers should only involve expressions of the form [a]18 with a an integer satisfying 0 a < 18. (a) compute [9]18 + [16]18. (b) compute [9]18[16]18. (c) compute [5] 1. 18 . (d) list the invertible elements of z18. (e) list the zero divisors of z18: [18 points] solve the system of simultaneous linear congruences: x 4 mod 24 x 7 mod 11.
