(b) Rabbi Elazar HaModai was his teacher, as stated in Sanhedrin, chapter 23 [(22a), and in the chapter of the oath of testimony and in Jerusalem Talmud, chapter 1 of Megillah, halacha 11, it is said in the name of Rabbi Elazar HaModai]. The genealogy is written [in the glosses of the Rema to the book Yesod Olam] that Rabbi Elazar ben Parta was a colleague of Rabbi Yochanan ben Zakkai, and afterwards it is written that he was a colleague of Rabbi.
Both cannot be correct; one who said in the name of Rabbi Elazar HaModai that he was his teacher, and Rabbi Elazar HaModai was a student of Rabbi Yochanan ben Zakkai. And even according to the opinion of the gloss in the genealogy that Rabbi Elazar HaModai was a colleague of Rabbi Yochanan ben Zakkai, it will ultimately not be possible for Rabbi Elazar ben Parta to be a colleague of Rabbi Yochanan ben Zakkai, and it is obvious that he cannot be a colleague of Rabbi who lived a long time after Rabbi Yochanan ben Zakkai.
We also find that Rabbi Shimon ben Elazar was a colleague of Rabbi, and Rabbi Elazar ben Parta said in his name. It appears that both were correct according to what I will write below, that there was another Rabbi Elazar ben Parta, the grandson of Rabbi Elazar ben Parta, thus it can be said that one was in the days of Rabbi Yochanan ben Zakkai and one was in the days of Rabbi. Rabbi Shimon ben Elazar, because of Rabbi Elazar ben Parta, who said in the name of Rabbi Elazar HaModai in Sanhedrin (22a).
In the Tosefta at the end of Sukkah, Rabbi Elazar ben Parta and Rabbi Elazar ben Yaakov say, etc. Abba Yossi ben Hanan says, etc. Rabbi Chanania ben Antigonus says, etc. Rabbi Yehuda says, etc.