Amar Pai’s Reviews > An Illustrated Theory of Numbers > Status Update
Amar Pai
is on page 193 of 323
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
— Jul 30, 2019 02:12PM
We're assembling the modular worlds.. the shadows of the integers
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Amar Pai
is on page 193 of 323
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
— Jul 30, 2019 02:10PM
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
