What 2 square numbers subtract to make 8564?

What two square numbers subtract to make 8564? In other words, when you subtract one square number from another square number, the answer is 8564. What are the two square numbers?

First, note that a square number is what you get when you multiply a number by itself, which means that the square root of a square number will equal a whole number. Thus, this is what we are solving:

A² - B² = 8564

We listed all square numbers up to one million. Then we tried all different combinations of subtracting one square number from another to see if we could get 8564. We could not find two square numbers that subtract to make 8564.

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What 2 square numbers subtract to make 8565?
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