If $v$ is odd, $k = 5\mod 8$, and $\lambda = 3\mod 4$ then there is no $(v, k, \lambda)$- symmetric balanced incomplete block design.
($\lambda$ is the index)
I know that $v$ is odd so I can show that the following equation can't me satisfied with integers $x, y,z$.
$$x^2 + (k-\lambda)y^2 + \lambda z^2 (-1)^{\frac{v-1}{2}} $$
How do I show that this equation can't be satisfied? I think this the way to go about proving this.