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 = (

) * (

) + (a_(k-1)) * (10^(k-1)) + ... + a * 10 + (

) *

and

s= (

) + (a_(k-1)) + ... + a + (

)

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

3 | (

) + (a_(k-1)) + ... + a + (

) <=> (

) + (a_(k-1)) + ... + a + (

) = 3 m

but then once again im lost in what to do

thankyou very much,

from an extremely stressed CoCo_RoAcH