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B Is there a theorem for this?

  1. Jul 8, 2016 #1
    "Write out a series of three or more different whole numbers in geometric progression, starting from one, so that the numbers should add up to a square. So like, 1 + 2 + 4 + 8 + 16 + 32 = 63 (one short of a square)"(can't find an actual real life example)

    I can't seem to find an answer for this?
     
  2. jcsd
  3. Jul 8, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Just use a spreadsheet to try some more, there are two three-digit examples.
     
  4. Jul 8, 2016 #3

    fresh_42

    Staff: Mentor

  5. Jul 8, 2016 #4
    1+3+9+27+81=121=11^2
     
  6. Jul 19, 2016 #5
    Try considering the sequence of squares, 0, 1, 4, 9, ..., and take the difference between subsequent squares. That will help you find the answer.
     
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