Where is there a discussion where the phrase "to be circumcised" means "to convert to Judaism" or "to become a Jew"?
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There is a sugya in Avoda Zara 10b where someone called Ketia bar Shalom successfully defended the Jews against Roman conspirators, but was nonetheless sentenced to death for having won the debate against the king. On his way to be killed a roman woman remarked that unfortunately he was being killed for defending the Jews but he would not get the same reward in the world to come since he was not circumcised. Whereupon he was circumcised.
Tosafos raised a contradiction that we said Antoninus would get reward in the world to come. Tosafos answer that he too was circumcised (נימול).
Tosafos go on to quote this from the Yerushalmi in the first chapter of Megilla (halacha 13). There we find the statement that Antoninus was circumcised and ends off saying 'this is the statement that Antoninus converted'.
א''ל אנטונינוס לרבי את מאכילני מן לויתן לעתיד לבא Antoninus said to Rabi will you give me to eat from the leviathan in the future? א''ל אין He (Rabi) responded yes. א''ל מן אימר פסחא לית את מאכילני ומן לויתן את מאכילני He (Antoninus) asked from a paschal sacrifice you will not feed me, but from the leviathon you will? א''ל מה אעביד לך דהא כתיב וכל ערל לא יאכל בו He (Rabi) said what can I do for you? It is written an uncircumcised may not eat of it. כיון דשמע כן אזל וגזר גרמיה Once he (Antoninus) heard this he went and cut himself. הדא אמרה איגייר אנטונינוס About this it is said Antoninus converted.
This Yerushalmi that Tosafos quotes definitely equated the term circumcised with converted, however if you look around in that sugya in Avoda Zara you will find later commentaries who don't think it's possible. Poras Yosef for instance raises the issue that a nonjew cannot perform a halakhicaly acceptable circumcision.