Bava Metzia, Chapter 2, Mishnah 6. After dealing with the obligation to announce a lost item, the Mishnah comes to clarify its parameters: how far does the finder's obligation to publicize his find extend, and from when may he say that he has fulfilled the Torah-mandated obligation to announce it?
On this question, there is a dispute between two fundamental approaches:
The approach of Rabbi Meir: It is sufficient that the local residents know about the find. They live in the area where the item was lost, and it likely was lost from them, therefore publicizing it among them is enough.
The approach of Rabbi Yehudah: The finder must make an effort and notify every Jew about it, and therefore he presents a completely different approach.
The text of the Mishnah:
"Ve'ad masai chayav lehachriz - ad sheyeidu bo shechenav, divrei Rabbi Meir" - how much time is incumbent upon the finder to continue and publicize the matter of the find? According to Rabbi Meir, until all his neighbors know about it, meaning all the residents of the place where the item was lost, since it was apparently lost from them.
"Rabbi Yehudah omer: shalosh regalim" - in his opinion this is not enough, and the finder must announce it specifically in Jerusalem, since everyone ascends there, and in this way one can reach every Jew. On the next three pilgrimage festivals, when all of Israel ascends to Jerusalem, it is incumbent upon him to publicize his find.
The reason that specifically three festivals were established is that not everyone is capable of ascending every time - there are the sick, and there are those whose circumstances beyond their control prevent them from ascending on a particular festival. But after three festivals - Pesach, Shavuos and Sukkos - the assumption is that everyone has already been in Jerusalem, and everyone has been given a fair opportunity.
Even Hato'en:
Furthermore, the Gemara in Tractate Taanis explains that there was a stone in Jerusalem called "Even Hato'en" - a sort of lost and found department, upon which they would claim ownership of items. Finders would arrive there, and losers would come there, and there they could locate their lost objects.
The Mishnah instructs that the announcement is made there on the three festivals, and on each of them the finder would publicize and announce the find. On the first festival he would say: I found a Megillas Esther, is it yours? And similarly on the second time. On the third time he would not note that this is the third time, but rather say as in the beginning: I found a Megillas Esther, is it yours?
"Ve'achar haregel ha'acharon shivah yamim":
The three festivals are not enough; rather, the finder must remain in Jerusalem for an additional seven days after the third festival, and the Mishnah details the calculation of the days:
"Kedei sheyelech leveito sheloshah" - A person who lost the scroll and is unaware of it needs to return home and check, and this journey may take three days. Although some live closer and some live further away, this is the timeframe that the Mishnah deemed sufficient.
"Veyachzor sheloshah" - Three additional days to return to Jerusalem.
"Veyachriz yom echad" - According to the Bartenura, the one who lost the item needs one day to locate the finder and say to him: Where is the man who found the scroll? It is mine, and I have its identifying marks.
This is the opinion of Rabbi Yehudah, and it is obviously based on the reality in which the Beis HaMikdash stands and the Jewish people make the pilgrimage.
Practical halachah: Nowadays, it has been established that it is sufficient to publicize in the local community where the item was found - hanging a notice in the synagogue or on a pole near the place where the object was found, and the like. Such publicizing is sufficient, as this is all that can practically be done.