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Positive integers $x$ and $y$ satisfy $x^{2} - y^{2} = 45$ . How many ordered pairs $(x, y)$ are there?

Competition practiceAlgebra

A3
B6
C2
D4

Step-by-Step Solution

(x - y) (x + y) = 45

with both factors odd and

x - y < x + y : 1 \times 45, 3 \times 15, 5 \times 9

, giving (23, 22), (9, 6), (7, 2). Three pairs.

Answer: A) 3

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