Question 73
We call a positive integer $n$ amazing if there exist positive integers $a, b, c$ such that the equality
$$
n = (b, c)(a, b c) + (c, a)(b, c a) + (a, b)(c, a b)
$$
holds. Prove that there exist $2011$ consecutive positive integers which are amazing. (By $(m, n)$ we denote the greatest common divisor of positive integers $m$ and $n$.)
$$
n = (b, c)(a, b c) + (c, a)(b, c a) + (a, b)(c, a b)
$$
holds. Prove that there exist $2011$ consecutive positive integers which are amazing. (By $(m, n)$ we denote the greatest common divisor of positive integers $m$ and $n$.)