Скачать или смотреть (4.1.21) Exhaustion Method: Expressing Even Integers Under 26 as Perfect Squares Sum

Hello everyone! In this video, we're going to use the method of exhaustion to prove a statement about positive even integers less than 26. Specifically, we're going to show that each of these integers can be expressed as a sum of three or fewer perfect squares.

We start with the smallest even integer, 2, and work our way up to 24. For each integer, we find a combination of perfect squares that add up to it. For example, 2 can be expressed as 1 squared plus 1 squared, and 4 can be expressed as 2 squared. We continue this process for all the even integers up to 24.

By the end of the video, we've shown that every positive even integer less than 26 can indeed be expressed as a sum of three or fewer perfect squares. This is a great example of how the method of exhaustion can be used to prove mathematical statements. Stay tuned for more videos where we explore these fascinating mathematical concepts!

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