The number of students in a school is between 500 and 600. If we group them into groups of 12, 20, or 36 each, 7 students are always left over. How many students are in this school?
Find the remainder when is divided by .
You may use the fact that is prime.
What is the remainder when is divided by
What is the remainder when is divided by
What is the smallest positive integer which is a multiple of 7, yet it gives a remainder of 1 when divided by any of 2, 3, 4, 5, or 6?