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If Am Israel went out of Egypt in 2448, 210 years after the moment yaakov avinu and the brothers joined yosef, that would be the year 2238. Yosef was 39 years old then and died at the age of 110. Means he died in the year 2309 after creation. According to Chazal Slavery in Egypt lasted 86 years 2448-86=2362

That means that there were 53 years between the death of Yosef and slavery.

In the light of that, how could one explain the Machloket (Sotah 11a) of Rav and Shmuel that מלך חדש in Shmot 1:8 (seemingly the one decreeing slavery) is the same Pharao as in the time of Yosef but he did as if he did not knew Yosef ?

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    What's the problem?
    – shmosel
    Mar 5 at 1:24

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Rashi in Parshas Vaeira 6:16 says that the slavery started after Levi passed away. This was 23 years after Yosef passed away (see sifsei chachamim there that makes the calculation, Levi was 4 years older than Yosef and died when he was 137 vs Yosef 110. This gives you 23 years).

So, which is it? Did the slavery start 23 years later or 53 years later? Was it 116 years long, or 86 years long?

The Seder Olam Perek 3 says that it was a gradual process that was at its peak for a minimum of 86 years and a maximum of 116. This means that the king that started the process, the one that they argue about in Sota, was only 23 years after Yosef.

Here is the words of the Seder Olam:

ויקם מלך חדש וגו' (שם), נמצא משמת לוי ועד שיצאו ישראל ממצרים קי"ו שנה, ואין השעבוד יותר על כן, ולא פחות מפ"ז שנים כשנותיה של מרים

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