Need help to prove project 7.14

Project 7.14. Prove the following divisibility test: n = 23:3)'1xi 10": is divisible by 7 if and only if (2)v(n)_1x0 +(2)v(")_2x1+(2)V(")_3x2 + ' ' ' + (2)xv(n)2 +xv(n)1 is divisible by 7. Generalize. Let m E Z20. By Theorem 7.7 and Proposition 7.9, for each i E Zzo such that 0 5 i S v(m) 1 there is a unique digit x,- such that m = [lily1x;- 10" and xv(m)_1 > 0. It is convenient (as we have all been taught since childhood) to represent m by the string of digits xv(m)_1xv(m)_2 - - -x2x1x0. For example, m=3-100+6-101+8-102+0-103+7-104 is represented by 70863. This string is called the base-ten representation of m. The following is a criterion for deciding when m