What 2 square numbers subtract to make 523?

What two square numbers subtract to make 523? In other words, when you subtract one square number from another square number, the answer is 523. 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 = 523

We solved the equation above and found this to be true:

262² - 261² = 523

262² is 68644 and 261² is 68121, therefore the answer to the question "What 2 square numbers subtract to make 523?" is 68644 and 68121 as illustrated below:

68644 - 68121 = 523

Note that there may be more than one solution to a problem like this. Above, we found the lowest combination of square numbers that subtract to 523. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 524?
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