I've been assigned the following homework problem:
Given an eight digit number $a_1a_2...a_8$ and a check digit $a_9$,
$7a_1+3a_2+9a_3+7a_4+3a_5+9a_6+7a_7+3a_8+9a_9 \equiv 0 \mod{10}$
This method detects all errors where only one digit is changed. Show that this is the case.
Can someone please point me in the right direction?