Impossibility for Byzantine Generals Problem where $n \leq 3m$
In the synchronous model of communication, there are $n$ agents which share a clock. In each round of communication, each agent sends an arbitrary message to each other agent, and then receives the message sent her by every other agent.

A protocol for byzantine agreement on $n$ agents supporting $m$ byzantine agents is a communication protocol for the agents satisfying the following properties:


Each agent receives an input bit.
The agents all start talking at time 0.
There are at most $m$ byzantine agents, whose behavior is arbitrary.
The other agents follow the protocol.
The protocol always terminates (this means that the non-byzantine agents always reach a special "terminate" state of the protocol, and then stop talking forever), with a return value which is also a bit.
The return values must all agree (note that this only applies to the non-byzantine agents).
If all input bits are the same, then the return values have to be the same bit.


The impossibility result states that such a protocol exists if and only if $n &gt; 3m$.

There is a different model in which an agent can sign a message, and this signature cannot be tampered with. In this model (which I will not specify formally) the problem can be solved for any $n,m$.

One of the difficulties in the area of distributed systems is the complicated nature of the computation model. If you want to understand the meaning of impossibility results, you have to familiarize yourself with these models in full detail (even more detail than the rather informal treatment in this answer).