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If no two numbers are alike, then there is no mode. The mode is none.
There are two modes. The mode is the only measure of central tendency where you can have no mode (no number appears more than another), one mode, or several modes, such as in your case.
If there is no repeated numbers there is simply no mode. If there is two numbers that are the same, (example: 3,3) then that will be your mode. (Data: 3,3 Mode:3)
Technically, every number that appear once is the mode (multiple modes). In practice however, it is best to not use the mode in this situation. If you divide the data in classes, one of the classes will be the mode of the new variable.
You list both.