I spent a lot of time trying to sovle this so I would really appreciate it if someone could just give me some hints what I am doing wrong.
There are positive intergers k, n, m such that
19/20 < 1/k + 1/n + 1/m < 1
What is the smallest possible value of k+n+m?
19 < 20 ( 1/k + 1/n + 1/m ) < 20
19 < 20 ( nm + km + kn/ knm ) < 20
nm + km + kn = try to make the value about 19.01
knm = 20
I did a lot of guessing and checking but now I am starting to see my solution doesn't make any sense..