MATH135 Study Guide - Midterm Guide: Surjective Function

In the following problems, we are the cyclic groups (Z_n, t) to investigate rules for integer divisibility. In what follows, we let m = a_k 10^k + a_k-1 10^k-1 + ... + a_2 10^2 + a_1 middot 10 + a_infinity be a positive integer written in decimal notation, so each a_j is a digit {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Devise a rule for divisibility by n = 5 Devise a rule for divisibility by n = 4 Devise a rule for divisibility by n = 11

Exercise 8. Let a b,t be positive integers, and assume that ar+ by for some r.y 2. Prove that (a, b) divides t.Hint: Use Proposition 1.1