Alice spent some time making sure he had a selection of $$strong primes$$ for her RSA parameters.

Since Alice and Bob are very friendly, Alice let Bob use some of this research. He in fact chose

one of Alices$$s primes pA $=$ pB $($but used a different qB$)$ in forming his modulus nB$.$

Just to $$be safe,$$ Bob and Alice chose different prime values for their exponents eA and eB$.$

If Eve suspects something like this and of course she has access to the publicly available nA$,$

nB and eA$,$ eB$,$ can she exploit this information and if so how?