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Math Help - positive integers x

  1. #1
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    positive integers x

    What are the positive integers x for which

    3^x + 4^x+ ... + (x+2)^x= (x+3)^x
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by perash View Post
    What are the positive integers x for which

    3^x + 4^x+ ... + (x+2)^x= (x+3)^x
    Wow, thats a tough question for pre algebra.

    I am not good enough to prove it, but the answers are going to be 2 and 3.
    3^2+4^2 = 9+16 = 25 = 5^2

    3^3+4^3+5^3 = 27+64+125 = 216 = 6^3

    After this, the (x+3)^x begins to outpace the sum of the lower powers, so it will continue to grow at a faster rate, and they won't ever catch back up. You can see it by charting the next few but like I said, I'm not good enough to prove it. Maybe someone else can prove it, I would love to see their thought process.
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