MATH 4023 Midterm: MATH 4023 LSU 4023s08 Exam 1
Document Summary
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: [15 points] use induction to prove that for every integer n 1, n. Hint: using part (a), make a table of all pairs m and n satisfying i. and ii. and see if this table contains a pair m and n satisfying iii: [15 points] this problem concerns arithmetic modulo 15. All answers should only involve expressions of the form [a]15 with a an integer satisfying 0 a < 15. (a) compute [7]15 [4]15. (b) compute [7]15[4]15. (c) compute [7] 1. 15 . (d) list the invertible elements of z15. (recall that invertible means multiplicatively invertible. ) (e) list the zero divisors of z15: [15 points] (a) state euler"s theorem concerning powers of a modulo n precisely. Be sure to carefully state the requisite hypotheses.
