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    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.
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    An example is enough to prove it.
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    I haven't got anywhere with an example, or a proof. It's tricky.
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    Hmm, keep looking.
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    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?
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    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.
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    Do you think it is the square of a rational or not?
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    (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.
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    (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.
    :yep:
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    Any ideas where to start?
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    (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
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    (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.
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    Any suggestions on where to start?
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    Already tried taking logs and got nowhere.
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    (Original post by DaveJ)
    But after the "is it ever?" question, it also asks to prove it.
    The proof is the example.
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    Does anyone actually have an example?
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    What do you understand by the term 'rational number'?
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    A number that can be expressed in the form (p/q)

    => 2^n + 3^n = (p/q)^2
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    Does anyone have an eample?
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    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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