Number Theory
# Divisibility

Find the digit \(N\) such that the three digit integer \( \overline{ 5 7 N} \) is a multiple of 9.

Find the digit \(N\) such that the five-digit number \(\overline{N878N}\) is divisible by 9.

How many 5 digit positive integers are multiples of 11, and have digits which sum to 43?