Question 169
At a party there are $1234$ participants, and each of them has shaken hands with exactly $137$ other participants. It is known that no three participants have shaken hands with each other. Furthermore, for any two participants $A$ and $B$ who have not shaken hands with each other, there must be exactly $k$ other participants who have shaken hands with both $A$ and $B$, where $k$ is a fixed constant. Find the value of $k$.