Gemara

2a - Mishnah: The first of Nisan is Rosh Hashanah for kings.

Rav Chisda: This pertains to documents:

Mishnah: Predated loan documents are invalid. Postdated documents are valid.

Beraisa: If a king began his reign on the 29th of Adar, Nisan 1 is considered his second year.

R. Yochanan: We learn that Nisan is Rosh Hashanah for kings from "Va'Yhi vi'Shemonim v'Arba Me'os Shanah l'Tzeis Benei Yisrael me'Eretz Mitzrayim ba'Shanah ha'Revi'is b'Chodesh Ziv Hu ha'Chodesh ha'Sheni li'Mloch Shlomo..." This equates Shlomo's reign to Yetzi'as Miztrayim. Just like Yetzi'as Miztrayim is counted from Nisan, also Shlomo's reign.

We know that Yetzi'as Miztrayim is counted from Nisan and not Tishrei, because Aharon died in Av in the 40th year (from Yetzi'as Miztrayim), and later Moshe addressed Benei Yisrael in Shevat of the 40th year.

3a - Objection: Perhaps the years are counted from Tamuz, Av or Adar!

Answer #2 (R. Elazar): We learn from "Va'Yachal Livnos ba'Chodesh ha'Sheni ba'Sheni bi'Shnas Arba l'Malchuso".

A Beraisa learns like R. Yochanan.

Avodah Zarah 10a: A case occurred, and a loan document was found. It was dated six years after the current date.

Rabanan: It is postdated. We should hold it and not allow the lender to collect until the date on it.

Rav Nachman: No, the date is for this year;

Most documents are dated from Yavan's supremacy. This scribe was precise, and dated it from the start of Yavan's rule, therefore the date is six years more than we normally write.

R. Yosi: Yavan ruled in Eilam for six years, then they conquered the world.

Question (Rav Acha bar Yakov): Perhaps the document was dated from Yetzi'as Miztrayim (which was exactly 1000 years before Yavan conquered the world); the scribe omitted the 1000, and only wrote the number of years above 1000. If so, it is postdated!

Answer (Rav Nachman): In Bavel, we date documents only from the reign of Yavan.

Support #1: Rav Acha bar Yakov found a Beraisa saying exactly like Rav Nachman.

Support #2 (Ravina -Mishnah): The first of Nisan is Rosh Hashanah for kings and festivals. The first of Tishrei is Rosh Hashanah for years and Shemitah;

Question: Rav Chisda said that Nisan 1 is Rosh Hashanah for kings regarding documents, and that Tishrei 1 is Rosh Hashanah for years regarding documents!

Answer: We count the years of Yisrael kings from Nisan, and of Nochri kings from Tishrei.

Summation of support: Every Tishrei we (in Bavel) add onto the year on our documents. If we counted from Yetzi'as Miztrayim, we would count from Nisan!

Rishonim

Rosh (Avodah Zarah 1:7): Rav Nachman assumed that the document was dated from the start of Yavan's rule, and allowed to collect from it. The Ri similarly was Machshir a document in which the hundreds and Prat (the remaining years less than 100) were written properly, but it does not say 'from Bri'as ha'Olam'. Rav Nachman assumes that a document was written unlike normal documents, rather than to say that the lender willingly postdated it and forfeited the right to collect from property sold in the interim. All the more so we may assume that a document was written like normal documents (nowadays, from Bri'as ha'Olam), rather than to say that it is postdated! Similarly, if the thousands were omitted the document is Kosher. Rav Acha suspected that the document was dated from the Churban. This shows that the thousands were not written, and still Rav Nachman was Machshir it!

Poskim

Shulchan Aruch (43:2): If the scribe omitted 'from Bri'as ha'Olam', and also did not write '5000 (years)', the document is Kosher.

Source (Beis Yosef (DH v'Da): The document Rav Nachman was Machshir did not mention any Malchus (we suggested that it was dated from the Churban) and it was also missing the thousands.

Shulchan Aruch: Even if he omitted the hundreds and only wrote the Prat, it is Kosher.

Shach (4): E.g. it says 80, and it is now the year 80.

Beis Yosef (DH v'Kosav): If also the tens were omitted and only the Prat (less than 10) was written, I am unsure whether or not it is Kosher. I lean to be Machshir.

Aruch ha'Shulchan (2): Since everyone dates from Bri'as ha'Olam, we do not suspect that he dated it from some other time.

Rebuttal (Benei Shmuel and Tif'eres Shmuel, brought in Hagahos in Tur ha'Shalem (15)): It is normal to omit the thousands and hundreds, but it is not normal to omit the tens!

Rema: If the thousands are written and also the small Prat, but the hundreds or tens are omitted, it is Pasul.