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If it’s sugarless it will not break your fast but chewing gum causes you to salivate and this causes your digestion to begin. This of course won’t hurt you or defeat your fast but it will most likely make you feel hungrier.
It may backfire and just make you more hungry. I suppose it depends on how long you’re planning to fast. In any case if you aren’t avoiding artificial sweeteners then you could give it a try and if it makes the hunger worse then you’ll know for next time. Remember, the hunger comes in waves and it will go away after not too long.