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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.

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    I know what it means to say that an *equation* can't be satisfied, but I don't know what you mean when you say that *expression* can't be satisfied.2012-03-08

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