Jacobian conjecture as a problem on integral points on affine curves

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$oftheform$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},$suchthattheaffinecurve$F_1(X)=F_2(X)=\dots=F_n(X)$ has no non-zero integer points.