Does the prayer of one who doubted the number of rak'ahs, completed it based on the lesser number, and forgot the prostration of forgetfulness (sujood as-sahw) become invalidated, and is it obligatory to repeat it?

If a worshipper forgets to perform the prostration of forgetfulness (sujud al-sahw) until a long time has passed or he has left the mosque, his prayer is valid, and he owes nothing. This is because it is a补救 for the worship, and the prayer is not invalidated by its omission.