Hello,

We know that for any positive integer a, divides (geometric sum)

Therefore :

-->

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Goin' back to the problem :

Note that this is the sum of the digits of the number.

This holds for any number (try it out with a,b,c,d,... as the digits, you will see the same conclusion)

This uses basic rules of modular arithmetic (and the previous question) :Suppose we want to compute the product 8215 x 3567 modulo 9. Replacing these numbers by those obtained by adding their digits and reducting modulo 9 gives 16 x 21 = 7 x 3 =21 = 3 (mod 9). Is it true that 8215 x 3567 = 3 (mod 9)? Explain