Number Theory in Discrete Mathematics

Question 1

is a branch of mathematics focused on the properties and relationships of numbers, particularly integers.

Answer 1

Number Theory

Question 2

A number a is divisible by b if there is an integer c such
that a=bc.

Answer 2

DIVISIBILITY AND PRIME NUMBERS

Question 3

• The largest positive integer that divides two integers
  without leaving a remainder.

Answer 3

GREATEST COMMON DIVISOR (GCD)

Question 4

A system of arithmetic for integers where numbers wrap
around upon reaching a certain value—the modulus.
a≡b (mod m) means m divides a−b.

Answer 4

MODULAR ARITHMETIC

Question 5

Equations that seek integer solutions.
Example: ax+by=c, where x and y are integers.

Answer 5

DIOPHANTINE EQUATIONS

Question 6

Uses properties of prime numbers and
modular arithmetic to encrypt and decrypt messages.

Answer 6

RSA Algorithm

Question 7

Relies on the arithmetic of
elliptic curves over finite fields.

Answer 7

Elliptic Curve Cryptography

Question 8

is integral to computer
science as it provides the mathematical
foundation for algorithms, data structures,
cryptography, and more.

Answer 8

Discrete mathematic

Question 9

Concepts like graphs, sets, and functions provide
abstract models to design algorithms and data structures.

Answer 9

Abstract Structures

Question 10

Discrete math instills rigor in problem-solving,
essential for ensuring the correctness and efficiency of algorithms.

Answer 10

Mathematical Rigor

Question 11

Understanding combinatorics and number theory is key to analyzing the computational complexity of algorithms.

Answer 11

Computational Complexity

Question 12

Number theory ensures the robustness of cryptographic protocols, vital for secure communication in computing systems.

Answer 12

Cryptographic Security