Recent content by nano1

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    MHB Solve Induction Problem: cn <= n log2n

    Hey I've been given an equality to solve as a bonus question with a strong hint that a like one would appear on my midterm. However, I am stumped by it, it appears quite complex to me. Any insight into how to solve this would be greatly appreciated! I'll try to type it as best I can: A student...
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    Oh forgot about including the a. Well, that looks like a contradiction right? Since both sides are identical yet it says it doesn't equal each other?
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    So that it now looks like k2 - k3 = k2 - k3 ?
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    It would be k2a - k3a cannot equal k1a
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    It wouldn't be k1a by any chance since it is the contradiction to your statement?
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    I think I've figured out the second question I posted at least but the contradiction that I'm trying to find for the one you're helping me with still is stumping me. I apologize, if I'm being irritating since you've already restated the steps twice.
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    Re: Extra practice help! I don't quite understand what the k is supposed to mean in your proof. Am I supposed to pick some number b and c and multiply it by a different number k? Sorry, math easily confuses me
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    MHB Can there be two positive integers x and y that satisfy x^2 - 4y^2 = 14?

    Hey, I've been stuck on these questions for awhile. They're bonus/ extra practice questions and I have a midterm coming up and I'm not quite comfortable with the process. If anyone can help me that'd be great! Prove the following theorem: for all integers a, b and c, if a does not divide b - c...