Find all triplets (A, B, C) of nonzero integers with A ≤ B ≤ C satisfying:

(1 + 1/A) (1 + 1/B) (1 + 1/C) = 3.

Prove that there are no others.

Note: There may be more than one solution.

(In reply to answer - spoiler by Ady TZIDON)

 There may be at least one more solution involving negative  and positive integers.

Posted by K Sengupta on 2013-07-20 11:47:05