What 2 square numbers subtract to make 8242?

What two square numbers subtract to make 8242? In other words, when you subtract one square number from another square number, the answer is 8242. 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 = 8242

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 8242. We could not find two square numbers that subtract to make 8242.

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What 2 square numbers subtract to make 8243?
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