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## Homework Statement

How many values of k can be determined in general, such that (k/p) = ((k+1) /p) = 1, where 1 =< k <=p-1?

Note: (k/p) and ((k+1)/p) are legendre symbols

Question is more clearer on the image attached.

## Homework Equations

On image.

## The Attempt at a Solution

I've tried C(7)=#{1} and it equals to 1 set or C(7) = 1 and

C(13) = #{3, 9} = 2

I also plugged in p = 4n+1 into C( p) which makes it equal n-1.

As well, p = 4k+3 into C( p) makes it equal to n.

This in fact does make the above equation of C( p) true. But how do I show that it works for all prime p that are odd?