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# Stuck on Proof watch

1. Is 2^n + 3^n (where n is an integer) ever the square of a rational number? Prove whether or not this so?????

Finding it borderline impossible to prove.
2. An example is enough to prove it.
3. I haven't got anywhere with an example, or a proof. It's tricky.
4. Hmm, keep looking.
5. What have you tried so far? And do you think 2^n + 3^n is the square of a rational number, or it isn't?
6. Bear in mind the question is whether it is the square of a rational number, not the whether it is the square of an integer.

EDIT: Lies (see later on) ---> Proving by example isn't really on, but disproving only requires one to break the rule.
7. Do you think it is the square of a rational or not?
8. (Original post by aKarma)
Proving by example isn't really on, but disproving only requires one to break the rule.
No. The question asks whether 2^n + 3^n is ever the square of a rational number, so just one example is sufficient. And a single counterexample won't disprove it.
9. (Original post by Glutamic Acid)
No. The question asks whether 2^n + 3^n is ever the square of a rational number, so just one example is sufficient. And a single counterexample won't disprove it.
10. Any ideas where to start?
11. (Original post by Glutamic Acid)
No. The question asks whether 2^n + 3^n is ever the square of a rational number, so just one example is sufficient. And a single counterexample won't disprove it.
My mistake, other way round here, proof by example is fair game
12. (Original post by Glutamic Acid)
No. The question asks whether 2^n + 3^n is ever the square of a rational number, so just one example is sufficient. And a single counterexample won't disprove it.
But after the "is it ever?" question, it also asks to prove it.
13. Any suggestions on where to start?
14. Already tried taking logs and got nowhere.
15. (Original post by DaveJ)
But after the "is it ever?" question, it also asks to prove it.
The proof is the example.
16. Does anyone actually have an example?
17. What do you understand by the term 'rational number'?
18. A number that can be expressed in the form (p/q)

=> 2^n + 3^n = (p/q)^2
19. Does anyone have an eample?
20. You don't need to algebraically solve it, only find an example. I was just checking whether you understood what one was.

All you need to do to prove it is find a case where the root of the outcome is rational (assuming you are using a calculator this probably won't actually show up as a fraction but can be expressed as such)

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