  It is shown that the $n$-dimensional Jacobian conjecture over algebraic
number fields may be considered as an existence problem of integral points on
affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is
false, then for some $n\gg 1$ there exists a counterexample $F\in
\mathbb{Z}[X]^n$ of the form $F_i(X)=X_i+ (a_{i1}X_1+\dots+a_{in}X_n)^{d_i}$,
$a_{ij}\in \Z$, $d_i=2;3 $, $i,j=\overline{1,n},$ such that the affine curve
$F_1(X)=F_2(X)=\dots=F_n(X)$ has no non-zero integer points.
