Prove there exists a consecutive pair of ints

[r0bHadz]

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.

 

[Orodruin]

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?

 

[r0bHadz]

I think the intent was indeed to demonstrate proof of existence by construction