### Instruction: What is the smallest positive four-digit integer equivalent to 6 mod 7?### Response: 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.
I notice that 1000 is equivalent to 6 mod 7, since 1000 = 7 \times 142 + 6.