Let r s k and n be integers with nk1 and let Gckf for some i

Let r, s, k and n be integers with n>k>1 and let G={[c]=[kf] for some integer f}. If [r] and [s] are in G, then both [r]+[s] and [r]*[s] are in G.

Solution

Given:

         r, s, k and n be integers with n>k>1

     Let G={[c]=[kf] for some integer f.

            here k is between 1 to n so,

                        in G={[c]=[kf] for some integer f.

                        take r in place of k then ok,

                G={[c]=[rf] for some integer f.

          and take s in place of k then ok,

                G={[c]=[sf] for some integer f.

    Now take r in place of k=r+s then ok,

                G={[c]=[kf] for some integer f.

   And Now take r in place of k=r*s then ok,

                G={[c]=[kf] for some integer f.

   In this way we say [r] and [s] are in G, then both [r]+[s] and [r]*[s] are in G.