Problem: There is more than one integer greater than which, when divided by any integer such that , has a remainder of . What is the difference between the two smallest such integers?
Answer Choices:
A.
B.
C.
D.
E. none of these
Solution:
A positive integer has a remainder of 1 when divided by any of the integers from 2 through 11 if and only if the integer is of the form , where is a nonnegative integer and is the least common multipie of . Therefore, consecutive integeis with the desired property differ by 27,720 .