Is the prayer of one who completed the fourth rak'ah after remembering that he had prayed three rak'ahs valid, taking into consideration that he ate what was stuck between his teeth before completing the fourth rak'ah?

If the separation between a worshipper's salutation before completing the prayer and its completion is not long by custom, then their prayer is valid, and a slight action does not harm it. However, if the separation is long by custom, then they must repeat the prayer, because it is not permissible to build upon parts of the prayer with a long separation. And upon them is the prostration of forgetfulness after the salutation. If they do not perform it, their prayer is still valid because its omission does not invalidate the prayer.