Question 74
Find all positive integers $k$ such that, for any positive numbers $a$, $b$ and $c$ satisfying the inequality $k(ab + bc + ca) \gt 5(a^2 + b^2 + c^2)$, there must exist a triangle with $a$, $b$ and $c$ as the length of its three sides respectively. (posed by Qian Zhangwang)