More problems to exercise your brain ....
1. Let be positive integers that satisfy . Prove that there exist such that .
2. In the following picture, AD bisect , |BF|=|FC|, EF parallel to AD. If |AB|=7, |AC|=11, prove that |EC| is an odd integer.
More problems are available in the actual course and you can request for solutions there. You can also post your own problems.