Find the smallest positive integer that leaves a remainder of 1 when divided by 2, 3, 4, 5, or 6, and is exactly divisible by 7.
Take any prime number greater than 3, square it, and subtract 1. Show that the result is always divisible by 24.
Pick any 2-digit number and subtract the number formed by reversing its digits (e.g., 73 − 37 = 36). The result is always divisible by what number?