7/5 = 1 remainder 2

0 mod 5 = 0- If you are only are interested in the remainder, the mathematical notation is: 7 mod 5 = 2
- You pronounce it as: 7 modulo 5 is congruent to 2
- In this example the value 5 is called the modulus
- The purpose of applying a modulo operation is to keep the resulting value (remainder) within a certain range.

1 mod 5 = 1

2 mod 5 = 2

3 mod 5 = 3

4 mod 5 = 4

5 mod 5 = 0

6 mod 5 = 1

7 mod 5 = 2

8 mod 5 = 3

9 mod 5 = 4

10 mod 5 = 0

11 mod 5 = 1

12 mod 5 = 2

13 mod 5 = 3

14 mod 5 = 4

- n mod p = "remainder" = {0.....p-1}
- Example: λ2 - x - xG (mod p)

The purpose of this blog is not to teach you how to do modulo arithmetic but just to explain what the purpose is of a modulo operation.

Example:

- 𝜆 = (yG - y) / (xG - x) (mod p)
- xR = 𝜆2 - x -xG (mod p)
- yR = 𝜆(x - xR) - y (mod p)

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