What is the smallest positive four-digit integer equivalent to 6 mod 7?
I want to find a number that leaves a remainder of 6 when divided by 7. One way to approach this is to start from the smallest four-digit number, 1000, and keep adding 1 until I get a multiple of 7 plus 6. This might take a long time, so I'll look for a shortcut. That means that 1000 already satisfies the condition, so it is the smallest positive four-digit integer equivalent to 6 mod 7.

