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When $x < N$, there cannot be the same encrypted message with different outgoing messages.

But why?

Passi
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    I think this might cover your answer; Does RSA work for any message M?. If it is not working, i.e. there might be two distinct messages that have the same ciphertext ( as one of the reasons) then the decryption is not possible, so RSA is not working for all message $M < N$. This is not the case. – kelalaka Mar 25 '22 at 20:33
  • Please indicate if this answers your question. In that case we might close the question as a dupe, in the safe knowledge that you might not have an original question, but that it is already in the little knowledgebase that is [se].. – Maarten Bodewes Mar 27 '22 at 16:26

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