hi, can somebody please help me with the following proof:
Let r be an odd prime. Show that there is an integer a such that
and
I know i need to consider the smallest positive quadratic nonresidue
mod r.
The first condition by itself is easy - try a=1.
[Something seems wrong if both conditions must hold at the same time - try r=7. The numbers mod 7 are 1,2,3,4,5,6 whose quadratic residues are:
1,4,2,2,4,1 and it doesn't look like any of them satisfy your 2 conditions.]
Ignore the above - misinterpreted the Legendre symbol.