What 2 square numbers subtract to make 127?

What two square numbers subtract to make 127? In other words, when you subtract one square number from another square number, the answer is 127. 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 = 127

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

64² - 63² = 127

64² is 4096 and 63² is 3969, therefore the answer to the question "What 2 square numbers subtract to make 127?" is 4096 and 3969 as illustrated below:

4096 - 3969 = 127

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 127. Below we list alternate solutions if available.

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What 2 square numbers subtract to make 128?
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