Question 164
For each positive integer $n$, consider the set
$$
T_n = \{ 11(h + k) + 10(n^h + n^k) \mid h, k \in \mathbb{N} \text{ and } 1 \le h \le k \le 10 \}.
$$
Find all positive integers $n$, such that the set $T_n$ has the following property: For all $a, b$ in $T_n$ with $a \ne b$, we always have $a - b$ is not divisible by $110$.
($N$ denotes the set of non-negative integers).
$$
T_n = \{ 11(h + k) + 10(n^h + n^k) \mid h, k \in \mathbb{N} \text{ and } 1 \le h \le k \le 10 \}.
$$
Find all positive integers $n$, such that the set $T_n$ has the following property: For all $a, b$ in $T_n$ with $a \ne b$, we always have $a - b$ is not divisible by $110$.
($N$ denotes the set of non-negative integers).