(8 points) We will find the smallest positive integer x that solves the following system of congruences via the Chinese Remainder Theorem: x7 mod 17 xE6 mod 11 x39 mod 43 In the language of Theorem 4 from page 236 of the 6th edition of Rosen, we thus have the values of the following variables: a1 and m3 a2 = 7 and m2 = 17 :: 6 and m3 11 as 39 and m443 The first step is to calculate m = mlm2m3m4 When we do this we get: The second step is to calculate the mi which are given by the formula mtheir values below Next we find the yi which are given by solving 1 mod m Thus for example, to find yi we need to solve 8041yi1 mod 3 Since we know 8041 1 mod 3, this simplifies to ly mod 3 Solve this either by trial and error or by using the Euclidean algorithm and enter the value of ibelow: (Use the canonical representative modulo 3.) Similarly, to find y we need to solve