2006 SMT/Algebra Problems/Problem 9
Problem
Principal Skinner is thinking of two integers and and bets Superintendent Chalmers that he will not be able to determine these integers with a single piece of information. Chalmers asks Skinner the numerical value of . From the value of this expression alone, he miraculously determines both and . What is the value of the above expression?
Solution
Let . Let and . Then,
.
Thus, for any given value of , we have another pair of integers such that . The only way in which this is not the case is if and , or and . Therefore, the value of the expression is .