Rath111
  • Rath111
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.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
You just have to show that such a pair indeed exists, so an example suffices. Did you use 0 and 1?
anonymous
  • anonymous
Other than that, I'm not sure how to (dis)prove this.
Rath111
  • Rath111
I used 8 and 9. 8 is 2^3 and 9 is 3^2

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Rath111
  • Rath111
Maybe guessing the example is just the way you go about proving it..
anonymous
  • anonymous
Yeah, the problem only wants one. That's proof enough for this kind of problem.
Rath111
  • Rath111
Meh, it just feels odd that this is the way to prove the problem. By guessing and writing down the example... But whatever, if that's all there is to it then so be it.
RadEn
  • RadEn
how about you with the numbers : 4^3 and 3^4 = (3^2)^2, is it allowed ?

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