Status Updates From An Illustrated Theory of Nu...

For any odd prime p, there are p-1 coprime integers (1 to p-1). Exactly half of these will be quadratic residues mod p. In the previous example where p is 11, there are 10 coprime integers - 1 2 3 4 5 6 7 8 9 - of which exactly 5 are quadratic residues. (1, 3, 4, 5, 9)

We're assembling the modular worlds.. the shadows of the integers

I've made it to quadratic residues, but the going is getting difficult. No fault of the book though. I feel like this is really as accessible as it can get. Just have to put the time in.

Quadratic residues mod 11 are 1, 3, 4, 5, 9:

1^2 = 1 mod 11
2^2 = 4 mod 11
3^2 = 9 mod 11
4^2 = 5 mod 11
5^2 = 4 mod 11
6^2 = 3 mod 11
7^2 = 5 mod 11
8^2 = 9 mod 11
9^2 = 4 mod 11
10^2 = 1 mod 11