Problem:
How many ordered pairs of integers satisfy the equation ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The equation may be rewritten as . Integers and are consecutive, so their product is a square of an integer if and only if one of them is 0 . Thus or , and the ordered pairs , and are the only ordered pairs of integers that satisfy the given equation.
The problems on this page are the property of the MAA's American Mathematics Competitions