Question: If instead, Alice used the same modulus as Bob nA = nB , ( but with different prime exponents eA and eB ) is there

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 Bobs RSA public keys would this help to determine
m?[Hint: the Euclidean algorithm on the exponents will help here .

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