Prove that there exists a pair of consecutive integers such that one of these integers is a perfect square and the other is a perfect cube.
(I guessed the integers to prove this, but I wanted to see if there was another way rather than guessing the two integers and writing them down as my proof.)

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You just have to show that such a pair indeed exists, so an example suffices. Did you use 0 and 1?

Other than that, I'm not sure how to (dis)prove this.

I used 8 and 9. 8 is 2^3 and 9 is 3^2

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