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Running on Zero

😃: Find a counterexample to the statement that every positive integer can be written as the sum of the squares of
three integers.
🤖: Sure! Here's an example of a positive integer that cannot be expressed as the sum of the squares of three integers:

50 = 1^2 + 4^2 + 9^2

But, 50 is not equal to 3^2 + 6^2 + 7^2. So, there exists at least one positive integer that cannot be written as the sum of the squares of three integers.