What 2 square numbers subtract to make 8269?

What two square numbers subtract to make 8269? In other words, when you subtract one square number from another square number, the answer is 8269. 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 = 8269

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 8269. We could not find two square numbers that subtract to make 8269.

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What 2 square numbers subtract to make 8270?
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