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It is shown that the $n$-dimensional Jacobian conjecture over algebraicnumber fields may be considered as an existence problem of integral points onaffine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ isfalse, 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.

Jacobian conjecture as a problem on integral points on affine curves