Find all possible triplets (a,b,c) of positive integers with a ≤ b ≤ c satisfying this equation:

2abc = ab + bc + ca +15

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)