The Archimedes Cattle problem should be mentioned here, see, for example http://web.archive.org/web/20070124203443/http://www.mcs.drexel.edu/~crorres/Archimedes/Cattle/Statement.html

Of course, the question can be asked whether this qualifies as a new result. (There is no way Archimedes or anyone else could write the answer).

In a modern interpretation, the mathematical result announced in this work is that every Pell's equation $x^2-ny^2-1$ where $n$ is not a square, has integer solutions. The first published proof is due to Lagrange.

The Archimedes Cattle problem should be mentioned here, see, for example http://web.archive.org/web/20070124203443/http://www.mcs.drexel.edu/~crorres/Archimedes/Cattle/Statement.html

Of course, the question can be asked whether this qualifies as a new result. (There is no way Archimedes or anyone else could write the answer).

In a modern interpretation, the mathematical result announced in this work is that every Pell's equation $x^2-ny^2=1$ where $n$ is a positive nonsquare integer has integral solutions with $y \not= 0$. The first published proof is due to Lagrange.

The Archimedes Cattle problem should be mentioned here, see, for example http://web.archive.org/web/20070124203443/http://www.mcs.drexel.edu/~crorres/Archimedes/Cattle/Statement.html

In the modern interpretation, the mathematical result announced in this work is that every Pell's equation $x^2-ny^2-1$ where $n$ is not a square, has integer solutions.

The Archimedes Cattle problem should be mentioned here, see, for example http://web.archive.org/web/20070124203443/http://www.mcs.drexel.edu/~crorres/Archimedes/Cattle/Statement.html

Of course, the question can be asked whether this qualifies as a new result. (There is no way Archimedes or anyone else could write the answer).

In a modern interpretation, the mathematical result announced in this work is that every Pell's equation $x^2-ny^2-1$ where $n$ is not a square, has integer solutions. The first published proof is due to Lagrange.