Must the Imam perform the prostration of forgetfulness (sujud al-sahw) if he doubts the number of rak'ahs and completes his prayer based on what he believes to be correct, while the congregants believe the prayer was valid?

Scholars have differed regarding acting upon the predominant assumption (ghalabat al-dhann) in prayer. The majority (jumhur) hold the view of building upon certainty (the lesser number of units) absolutely, citing the hadith of Abu Sa'id as their evidence.

Whereas Abu Hanifah and, in one narration, Ahmad, made a distinction: whoever has a predominant assumption acts upon it and prostrates (for forgetfulness) after the salām, and whoever is in doubt builds upon the lesser number and prostrates before the salām, citing the hadith of Ibn Mas'ud as their evidence.

Accordingly, if you deem it permissible to act upon the predominant assumption or follow someone who issues a fatwa to that effect, then you may do so. The prescribed prostration of forgetfulness (sujud al-sahw) in this case is after the salām, and the issue should be explained to the congregants (ma'mumin).