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 + ( ) *
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