Prove there exists a consecutive pair of ints

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SUMMARY

This discussion centers on proving the existence of a consecutive pair of integers where one is a perfect square and the other is a perfect cube. The example provided includes the integers 0 (perfect square) and 1 (perfect cube), as well as 8 and 9. The intent of the problem is to illustrate the principle of proof of existence by construction, emphasizing the importance of understanding the problem's context and formulation.

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Homework Statement


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.

Homework Equations

The Attempt at a Solution


I got 0 for perfect square and 1 for perfect cube.

Is this a trick or something? Maybe this wouldn't constitute as a proof?The problem is suppose to be a bit harder judging by the problem before and after it.
 
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It might be helpful to consider why you are being asked the question. Of course it is not difficult to come up with examples (8 and 9 being another), but the intent may be to demonstrate the principle of proof of existence by constuction. Only you know the context in which you were asked the question.

The alternative is that you missed part of the formulation. Did you reproduce it exactly as stated?
 
I think the intent was indeed to demonstrate proof of existence by construction
 

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