# Problem

Number Theory Level pending

Let $$a$$,$$b$$,$$c$$ be positive integers such that $$a$$,$$b$$,$$c$$ $$>1$$ and: $$a\mid bc+1 ,$$ $$c\mid ab+1 ,$$$$b\mid ac+1 ,$$ , if $$(a_i ,b_i,c_i)$$ are solutions find: $$\sum (a_i + b_i +c_i)$$.

×