Common-modulus RSA attack

If the same invertible message $m$ is sent under one RSA modulus with coprime public exponents $e_1,e_2$, choose integers $a,b$ with $a{e}_1+b{e}_2=1$. From $c_i=m^{e_i}(\mathrm{mod}N)$ one recoversusing modular inverses for negative exponents.