MATH135 Study Guide - Final Guide: Public-Key Cryptography, Chinese Remainder Theorem, Binomial Theorem

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: All

Document Summary

Pages: this test contains 9 pages, including this cover sheet and a page at the end for rough work. Id number, and circle your section, at the top of this page. If you need more space to show your work, then use the back of the previous page. 1: (a) let a0 = 1 and a1 = 3, and for n 2 let an = 3an 1 2an 2 1. Show that an = 2n +n for all n 0. [4] (b) find the term containing x8 in the binomial expansion of (cid:16) 18 x x2. 2: (a) let a = 215 and b = 17. Find the integers q and r wth 0 r < b such that a = qb + r. [7] (b) list all pairs of integers (x, y) with |x| 50 such that 245x + 189y = 84. 3: (a) list all elements [x] z13 such that [5][x]2 = [6].