The dispute of Rav Sadya Gaon [Rasag] and Rebbe Ahron Ben Meir of Eretz Yisrael:
In the times of Rav Sadya Gaon [882-942] erupted one of the most infamous disputes with regards to the Jewish calendar that threatened a catastrophic split amongst the Jewish people regarding the dates of Rosh Chodesh and the subsequent Holidays. The precise date of the debate was in year 921  and impacted the years 921-924. If, Heaven forefend, this dispute would not have come to a closure there would be different dates in which Jews celebrated the new months and the Holidays; while one Jew would celebrate Rosh Hashanah on Monday, another might celebrate Rosh Hashanah on Tuesday, depending on which opinion in the debate he decided to follow. The debate threatened to end the consensus of all Jewry as to the dates of Rosh Chodesh and the Holidays. What was the topic of debate? The debate surrounded the day of Rosh Hashanah and as to when on the calendar it is to be set. Earlier we explained that Rosh Hashanah cannot fall on certain days of the week and likewise cannot fall on the Molad Zakein. These matters are not up for debate and had consensus of all Jewry. What was debatable however was the precise definition of the Molad Zakein. How long after midday is a Molad considered a Molad Zakein which causes Rosh Hashanah to be differed to the next day? This was the subject of debate between Rav Sadya Gaon and Ben Meir. We will attempt here to give a general summary of this debate:
The position of Rav Sadya Gaon [Rasag]:
Rav Sadya Gaon [i.e. Rasag] was the leading Rabbinical figure of Bavel in the 900’s and was considered the absolute leader of Babylonian Jewry together with the Rosh Galusa, Ben Zakaiy. The Rasag held, as did most of Jewry, that a Molad Zakein begins immediately after midday, which is 18 hours from the previous night. This means that if the Molad of Tishrei falls prior to midday [18 hours into that day] then Rosh Hashanah is to be set on the day of the Molad. If however it falls after midday then the concept of Molad Zakein is in effect and Rosh Hashanah is delayed until the next day. [See Halacha G!]
The year of debate: In the year 923/4684 the Molad fell on Shabbos, 237 Chalakim [13 minutes] after midday. According to the Rasag, due to the Molad Zakein, Rosh Hashanah had to be pushed to Monday. In order to organize the calendar accordingly, the year 921/4682 had to be a Shleima [with 30 days in both Cheshvan and Kisleiv]. This caused Pesach of 4682 to fall on Tuesday.
The position of Ben Meir:
Rav Ahron Ben Meir was the leading Rabbinical figure of Eretz Yisrael in the 900’s. He held a tradition that a Molad Zakein only begins 642 Chalakim after midday, which is 35.5 minutes after midday. This means that if the Molad of Tishrei falls prior to 35.5 minutes after midday [18 hours and 35.5 minutes into that day] then Rosh Hashanah is to be set on the day of the Molad. If however it falls after the 35.5 minutes after midday then the concept of Molad Zakein is in effect and Rosh Hashanah is delayed until the next day. The Rasag argued that there is no basis in our tradition for the opinion of Ben Meir, and so was held by the majority of Jewry. Ben Meir however countered that he was the leader of Eretz Yisrael and the setting of the new month was given only to the Sages of Eretz Yisrael and hence the Rasag has no right to argue on his ruling.
The year of debate: In the year 923/4684 the Molad fell on Shabbos, 237 Chalakim [13 minutes] after midday. According to Ben Meir, due to it not being considered a Molad Zakein in his opinion, Rosh Hashanah would be on Shabbos, two days earlier than the Rosh Hashanah of the Rasag. Now, in order to organize the calendar accordingly, the year 921/4682 had to be a Chaseira [with 29 days in both Cheshvan and Kisleiv]. This caused Pesach of 4682 to fall on Sunday.
The outcome of the debate:
During the year of the debate in 921/4682 the residents of Bavel and majority of the Diaspora celebrated Pesach on Tuesday, as directed the Rasag, while the residents of Eretz Yisrael celebrated Pesach on Sunday as directed Ben Meir. This threatened to split the global Jewish community and confuse the dates of all the holidays. The Sages of Bavel implored Ben Meir to retract his position in face of the great calamity this would befall the Jewish people, although to avail. Ben Meir wrote counter arguments and vehemently argued that it is the Rasag who has to back down from his position, as he was the leader of Eretz Yisrael and held the sole jurisdiction in the matter of the Luach. Ben Meir viewed the Rasag as the sole person responsible for the dispute and the great calamity that it threatened. Seeing that Ben Meir would not back down, the camp of the Rasag then went on to a worldwide campaign to convince world Jewry to reject the position of Ben Meir and so it was that even the Sages of Eretz Yisrael adapted the ruling of the Rasag. This dispute came to end by the year 4684, as by that year even the residents of Eretz Yisrael adapted the ruling of the Rasag and this is the final ruling today which we follow in our calendar.
 Based on the correspondence of letters between the Rasag and Ben Meir recently discovered in Geniza Mitzrayim and published in the Sefer “Hamachlokes” of Rav Chaim Yechiel Borenshtein [Poland 1904, author of Simas Ayin]; Torah Shleima 13/9