  The Einstein equation for the Friedmann-Robertson-Walker metric plays a
fundamental role in cosmology. The direct search of the exact solutions of the
Einstein equation even in this simple metric case is sometime a hard job.
Therefore, it is useful to construct solutions of the Einstein equation using a
known solutions of some other equations which are equivalent or related to the
Einstein equation. In this work, we establish the relationship the Einstein
equation with two other famous equations namely the Ramanujan equation and the
Chazy equation. Both these two equations play an imporatant role in the number
theory. Using the known solutions of the Ramanujan and Chazy equations, we find
the corresponding solutions of the Einstein equation. The relationship between
the Friedmann equation and the equations of the trefoil knot and figure-eight
knot is established.
