What 2 square numbers subtract to make 257?

What two square numbers subtract to make 257? In other words, when you subtract one square number from another square number, the answer is 257. 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 = 257

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

129² - 128² = 257

129² is 16641 and 128² is 16384, therefore the answer to the question "What 2 square numbers subtract to make 257?" is 16641 and 16384 as illustrated below:

16641 - 16384 = 257

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 257. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 258?
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