Chapter 31.2, Problem 7E

Program Plan Intro

To define $\gcd$ function for over $2$ arguments by recursive expression $\gcd (a_0,a_1,\mathrm{....},a_n)=\gcd (a_0,\gcd (a_1,a_2,\mathrm{....},a_n))$ and demonstrate that $\gcd$ function returns similar solution independent of sequence in which arguments are stated. To also demonstrate how to discover integers $x_0,x_1,\mathrm{.....},x_n$ so that $\gcd (a_0,a_1,\mathrm{....},a_n)=a_0{x}_0+a_1{x}_1+\mathrm{......}+a_n{x}_n.$ To show that count of divisions done by the algorithm is $O(n+\lg \{\max \{a_0,a_1,\mathrm{....},a_n\})).$