## 21 Jun Few problems - 4

Find all integers $$ a,b,c $$ satisfying $$1<a<b<c$$ such that $$(a-1)(b-1)(c-1)$$ is a divisor of $$abc-1$$. Find the number of ordered pairs $$(x,y)$$ of positive integers which satisfy $$xy=27027$$. The integer $$N$$ consists of 2017 consecutive nines. A computer calculates $$N^3 = (999 ....