— “
is congruent to
modulo
” — means that
divided by
gives the same remainder as
divided by
.
i.e. , because
and
If then
Problem: Show that an integer is divisible by
if and only if the sum of its digits is divisible by
.
Solution: Call the digits of the integer
from left to right 
, so


Solution: Call the digits of the integer



i.e. is divisible by
exactly when the sum of its digits are.