Proposition:
Given a positive integer $n \geq 2$ and an $n-$dimensional vector $v=(v_1, v_2, \dots, v_n)\in \mathbb{Z}^n$, with the vector satisfying the following properties:
$v_i > b$ for $i=0,1,2, \dots , n$ and a fixed $b\in \mathbb{N}$
the set $\{v_1, v_2, \dots, v_n\}$ is pairwise relatively prime, i.e. $gcd(v_i, v_j) = 1$ for $i, j \in \{1, 2, \dots , n\}$
Then the linear Diophantine equation $\sum_{i=1}^{n}v_ix_i = 0$ only admits zero solutions ($x_i = 0$) with the constraints $|x_i| \leq b$
It is certainly ture for $n=2$, what about the case $n \geq 3$?