Problem:
The numbers and are a pair of consecutive positive perfect squares whose difference is . How many pairs of consecutive positive perfect squares have a difference of less than or equal to ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the consecutive positive perfect squares are and , then their difference is . Solving gives , so there are pairs of consecutive positive square pairs whose difference is less than or equal to 2023 , namely , $
The problems on this page are the property of the MAA's American Mathematics Competitions