AMC 10B 2023 (Problem 14)
How many ordered pairs of integers satisfy ?
Use Toolkit 6 — Square of a sum on the right-hand side of the equation in Hint 2.
Case 1:
Adding the equations gives
If , then
Similarly, if , then .
So this case gives ordered pair.
Adding the equations gives
If , then
Similarly, if , then .
So this case gives ordered pair.
Case 2:
Adding the equations gives
So this case gives ordered pairs.
Adding the equations gives
So this case gives ordered pairs.
(C)