- #1

- 201

- 2

- I
- Thread starter matqkks
- Start date

- #1

- 201

- 2

- #2

Ssnow

Gold Member

- 532

- 156

In mathematics they are used for the computation of Legendre symbols and for the proof when a number is expressible as sum of two squares ...

Ssnow

- #3

Stephen Tashi

Science Advisor

- 7,569

- 1,465

If the class has studied linear congruences then purely mathematical curiosity leads to asking about polynomial congruences. The simplest example would be ##x^2 = A (mod\ M)## I haven't studied this topic. A blog by John Cook https://www.johndcook.com/blog/quadratic_congruences/ deals with it.They have done Diophantine equations, solved linear congruences

I wonder if any application of quadratic residues to a practical topic comes by way of needing to solve ##x^2 = A (mod \ M)##.

The solutions to the quadratic equation ##x^2 = -1## play a crucial role in the theory of solving general polynomial equations over the real numbers. I wonder if the solutions to ##x^2 = A (mod\ N)## play a crucial role in the theory of solving general polynomial equations over the integers in mod N arithmetic. Can anybody comment on that?primitive roots.

- Replies
- 5

- Views
- 510

- Last Post

- Replies
- 3

- Views
- 946

- Replies
- 2

- Views
- 1K

- Replies
- 10

- Views
- 4K

- Replies
- 2

- Views
- 443

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 5

- Views
- 3K

- Last Post

- Replies
- 1

- Views
- 1K