Prove that is unsolvable if .
To determine whether the given number is quadratic residue , consider the list :
If the number of the elements in the above list lying between and inclusively is even , then is quadratic residue , otherwise , it is quadratic non-residue .
In this case , and is either or
The elements lying between the range should be :
for so the number is an odd number .
for so the number is also an odd .
Therefore , is not the quadratic residue of modulo .
Remarks : so we can see that is quadratic residue of modulo .