



 
Ben, You need to think about what a number like 9826 means. 9823 = 9(10^3) + 8(10^2) + 2(10) + 6 = 9(999+1) + 8(99+1) + 2(9+1) + 6 = 9(999) + 8(99) + 2(9) + 9 + 8 + 2 + 6, now clearly all the terms with all the '9's' in them are a multiple of 3 so the original number is a multiple of 3 if and only if 9 + 8 + 2 + 6 is a multiple of 3. To use induction you would induct on the number of digits  at the induction step you would pull off the 1st digit and it accompanying power of 10 and apply the induction hypothesis to the rest. Penny
 


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