Find all sets of integers A, B, and C which satisfy the following:
1/A + 1/B + 1/C = 1.
(In reply to
solution? by Charlie)
Yes, that's the complete solution. It's pretty straightforward to prove.
Let's assume that we are not interested in permutations and define A<=B<=C.
Now, since 1/A, 1/B and 1/C have to be 1/3 on average, A (the smallest number of the solution) has to be either 2 or 3.
For A=3, {3, 3, 3} is obviously the only solution.
For A=2, 1/B and 1/C have to be 1/4 on average, so B has to be either 3 or 4 (2 obviously doesn't work), so {2, 3, 6} and {2, 4, 4} are the only remaining solutions.
re: solution?
