- #1
imranq
- 57
- 1
Homework Statement
Find the number of roots for the equation [tex]x^2+1=0 \mod n \: for \: n = 8,9,10,45[/tex]
Homework Equations
The Attempt at a Solution
I have no idea where to start. Could someone help me understand?
Modular arithmetic is a type of arithmetic that deals with integers and their remainders when divided by a fixed integer. It is often used in number theory and cryptography.
The main difference is that in modular arithmetic, numbers "wrap around" when they reach the fixed integer, instead of continuing to increase. For example, in regular arithmetic, 5 + 7 = 12, but in modular arithmetic with a modulus of 10, 5 + 7 = 2.
Modular arithmetic is used in cryptography to encrypt information. By using modular arithmetic operations, such as modular exponentiation, secret messages can be encoded in a way that can only be decoded by someone who knows the appropriate key.
Prime numbers play a crucial role in modular arithmetic, as they are used to determine the modulus. Additionally, the properties of prime numbers are important when solving certain types of modular arithmetic problems.
Modular arithmetic has many real-life applications, such as in computer science, cryptography, and engineering. It is used in computer algorithms, error-correcting codes, and in the design of secure communication systems, among others.