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Plews Conjecture 1

  1. Jul 21, 2015 #1
    The following popped into my head and I am curious whether it is already a known relationship and whether it has an utility in math/physics. It is a follows: Where x and y are consecutive, whole numbers, the following is true: x + y = y2 - x2
     
  2. jcsd
  3. Jul 21, 2015 #2

    TeethWhitener

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    If x and y are consecutive, then y=x+1.
    x+y=x+x+1=2x+1
    y2-x2=(x+1)2-x2=x2+2x+1-x2=2x+1
    The proof is trivial. I can't think of any immediate application in math or physics.
    (For a slightly less trivial, but much intuitively prettier proof, think about this geometrically as a difference of the areas of two squares with sides x and x+1.)
     
  4. Jul 21, 2015 #3

    mfb

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    Or, even shorter: y2-x2 = (y-x)(y+x)
    By definition y-x=1, so y2-x2 = (y-x)(y+x) = y+x = x+y.

    Nothing new.
     
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