4. (15 points) Divisibility by 7. A number is divisible by 7 if the result of doubling the last digit and subtracting it from the rest of the number is divisible by 7.(This procedure can be applied again an again.) We will use this rule for the number 2422. Its last digit is 2, so we compute Now we do it again: 242 (2 x 2) = 242 - 4 = 238 23 (2 x 8) = 23 - 16 = 7 - 7 is divisible by 7, so 2422 is divisible by 7. Write a proof for this divisibility rule.