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
.