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Verify and prove (Posted on 2017-12-10) Difficulty: 4 of 5
Consider:
      (15 + 25)     +     (17 + 27)     =   2 *(1 + 2)4   
   (15 + 25 + 35)   +   (17 + 27 + 37)   =  2 *(1 + 2 + 3)4 
(15 + 25 + 35 + 45) + (17 + 27 + 37 + 47) = 2 *(1 + 2 + 3 + 4)4
       ...                  ...       and so on     ...

First, verify that both sides are equal for further increase in n,

then prove it.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: computer verification no proof ... or, come to think about it ... | Comment 2 of 5 |
(In reply to computer verification no proof by Charlie)

The LHS is a 7th degree polynomial in n, and the RHS is an 8th degree polynomial (what's inside the parentheses is a quadratic).  An 8th degree polynomial or lower is determined (or over-determined) by 9 points on it. We have 24 points shown on the polynomials--more than enough to show (prove) they're the same.
  Posted by Charlie on 2017-12-10 10:32:30

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