Suppose that a=(rn x rn-1 ... r2 x r1 x r0) 10^3. This notation means that a = 10^(3n) x rn + 10^3(n-1) x rn-1 + 10^3 x r1 + r0. Prove that 13|a if and only if 13|r0-r1+r2-r3+...+(-1)^nrn