# Cyclic powers of 2! IMO 2015 problem#2

**Number Theory**Level 5

Find all positive unordered multi-sets of integers \((a,b,c)\) such that \({ab-c,bc-a,ca-b}\) are powers of 2.

If these sets can be represented as \[(a_1,b_1,c_1),(a_2,b_2,c_2),\dots,(a_n,b_n,c_n).\] Evaluate \(\displaystyle\large{\left(\sum_{i=1}^{n} a_i + b_i + c_i\right) +n}\).