Problem of the Month
Hint for Problem 0: September 2022

1. No hint given.

2. What are the remainders when \(100\) and \(10\) are divided by \(7\)?

3. No hint given.

4. Try to find a condition on six-digit integers that detects divisibility by \(7\). There is a well-known general test for divisibility by \(7\), but it will be useful to find another one that is specific to six-digit integers and similar to the condition for three-digit integers implied by (b) and (c).