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Product and Pair Sum Puzzle (Posted on 2015-06-28) Difficulty: 3 of 5
Find all possible triplets (a,b,c) of positive integers with a ≤ b ≤ c satisfying this equation:

2abc = ab + bc + ca +15

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution By Hand (spoiler) Comment 1 of 1
1) It is obvious from inspection that either two or three of a,b,c must be odd

2) a must be less than 3.
To see this, let a = b = c = 3
Then the LHS = 54 and the RHS = 42.
Any increase in b and or c just makes the LHS increase more than the RHS.

3) It does not take long to find all solutions.
(1,2,17)
(1,3,9)
(1,5,5)
(2,3,3)

  Posted by Steve Herman on 2015-06-28 11:01:25
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