Arithmetic crosscorrelation of binary $m$-sequences with coprime periods

The arithmetic crosscorrelation of binary $m$-sequences with coprime periods $2^{n_1}-1$ and $2^{n_2}-1$\ ($\gcd (n_1,n_2)=1$) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary $m$-sequences is not greater than $2^{\min (n_1,n_2)}-1$.