The following exercise problem is from the book of D.B.West which i could solve:
If a complete graph can be decomposed into triangles then $n-1$ or $n-3$ is divisible by 6.
So my questions are the following,
If a complete graph of $n$ vertices can be decomposed into cliques of size $p$ with $p\leq n$ then what should be the relation between $n$ and $p$.
What is the official name of this problem in the literature ?
Any links/hints would be helpful.