The question is this.
Suppose that p is a prime, $p\ge7$. Show that $(\frac np)=(\frac {n+1}p)=1$ for at least one number n in the set {1,2,...,9}.
I think seperating into two cases when n=1 and when n=4 will help me prove it. But I can't think further...
Plz, HELP ME!!!!
Assume that the statement is not true. We clearly have $\left(\frac{1}{p}\right) = \left(\frac{4}{p}\right) = \left(\frac{9}{p}\right) = 1$. By assumption we must then have $\left(\frac{2}{p}\right) = \left(\frac{5}{p}\right) = \left(\frac{10}{p}\right) = -1$. Can you derive a contradiction from this?