If instead, Alice used the same modulus as Bob nA $=$ nB $,($but with different prime exponents

eA and eB $)$ is there now a weakness? If$,$ for example, Eve intercepted the same message m

encrypted as cA and cB using Alice and Bob$$s RSA public keys would this help to determine

m$?[$Hint: the Euclidean algorithm on the exponents will help here $.$