Regarding the year of Jesus' birth, it says in Seder HaDoros (Year 3724) that the year 3724 and the year (3)532 are really the same. What in the world does he mean?
Its in the first column first paragraph...
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He is saying that the year 3724 coincides with the end of a 532-year calendrical cycle. This cycle is when the 19-year machzor katan and the 28-year machzor gadol return to their initial positions (19 x 28 = 532). The year 3724 comes after exactly 7 of those cycles (532 x 7 = 3724). He does not explain why this has any significance.
UPDATE: Mevaqesh's comment spurred me to investigate further into the meaning of this cryptic statement, and I think I've ב"ה gotten to the bottom of it. Seder Hadoros is quoting the medieval work Tzemach Dovid, which at its source states that the author found the following short rhyme in an ancient manuscript:
בשנת ג' אלפים תשכ"ד הנוצרי נלכד, ובשנת תקל"ב בעץ נצלב
(Roughly: In the year 3724 the Nazarene was captured, and in the year 532 he was hanged.)
At first glance this doesn't seem to make sense, because the year 532 (or even 3532) is earlier than 3724. He therefore explains that "532" doesn't refer to the actual year, but rather describes the occurrence in terms of the calendrical cycle. In actuality, both events happened in the same year, which was 3724 from creation, and also came at the end of a full 532-year cycle (as explained above). By using these figures, each half of the sentence rhymes an event with the number that describes when it occurred. (תשכ"ד - נלכד, תקל"ב - נצלב).
[It still seems very strange - what was the point of all this? My hunch is that it had nothing to do with Jesus per se, but was simply a mnemonic device to assist the people of that time in making the calculations relating to the Jewish calendar. When doing these calculations, it is much easier to start reckoning from a recent year that began a new cycle, instead of having to start at year zero. Since 3724 was a year that coincided with the beginning of both the machzor katan and the machzor gadol, that was a convenient year to use as a starting point. In later generations one could just keep adding 532 to get to the next such years (e.g. 4256, 4788...). To help remember these two numbers, someone came up with a witty rhyme that would stick in people's minds.]
Getting back to Seder Hadoros, there is evidently some censorship and / or printing error: Instead of נלכד (captured) it says נולד (born), and instead of נצלב (hanged) it says וחי עד (and lived until), which basically makes the whole thing incomprehensible. Interestingly, I found a different edition of Tzemach Dovid in which a few critical lines are missing, clearly due to censorship issues.