Since the access code is sent to the telephone number which you're registering, you must have an active phone number in order to receive the access code. This can also be a temporary number, used only for the setup of Viber. e.g. phone card, landline etc.
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I do not think that you can use Viber without a phone number. The application does not create an account and thus uses your phone number as your identity to allow you make free Viber call to your friends using their phone numbers.
My daughter set up Viber before she left for East Africa using her AT&T mobile number. She asked me to disconnect her service with AT&T because she'll be gone a while and not be using her service and wanted to use a different provider when she returns. I did cancel it but she is still able to use her phone though Viber to call and text me. I don't get it but it does work without a working phone number at least for now. I checked with AT&T to make sure the service was cancelled and it is. Does anyone know why? Seems strange!