Question 1003366
*[tex \Large 100a + 10b + a = 101a + 10b]

*[tex \Large = (98a + 7b) + (3a + 3b)]

Since 98a+7b is always divisible by 7, we only need to check if 3a + 3b is divisible by 7. Since 3 and 7 are relatively prime, this occurs if and only if a+b is divisible by 7.

More formally, we say that *[tex \Large 101a + 10b \equiv 3a + 3b \pmod{7}].