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**CoCo_RoAcH** hey! the question is as follows:

Show that 3|n if and only if 3|s, where s is the sum of the digits of n (expressed as usual in base 10).

i was wondering if some one could please give me a hint as how to start off or give me a push in the right direction as i don't have any idea how to start(go about the question).

However, i do know that i need to show that 3|s and if this is true then 3|n will hold true as 3|n <=> 3|s.

plus i know that

n = ($\displaystyle a_k$) * ($\displaystyle 10^k$) + (a_(k-1)) * (10^(k-1)) + ... + a * 10 + ($\displaystyle a_0$) * $\displaystyle 10^0$

and

s= ($\displaystyle a_k$) + (a_(k-1)) + ... + a + ($\displaystyle a_0$)

oh and i was thinking that i may need to use the definition of divisibility where x|y <=> y = xn as

3 | ($\displaystyle a_k$) + (a_(k-1)) + ... + a + ($\displaystyle a_0$) <=> ($\displaystyle a_k$) + (a_(k-1)) + ... + a + ($\displaystyle a_0$) = 3 m

but then once again im lost in what to do

thankyou very much,

from an extremely stressed CoCo_RoAcH