Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. This tutorial will cover some of the basic concepts and results in number theory.
Basic Concepts
Prime Numbers: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.
Composite Numbers: A composite number is a positive integer that has at least one positive divisor other than one or itself. For example, 4, 6, and 8 are composite numbers.
Fermat's Little Theorem: If ( p ) is a prime number and ( a ) is an integer not divisible by ( p ), then ( a^{p-1} \equiv 1 \mod p ).
Interesting Facts
The number 7 is the only prime number that is also the sum of the cubes of its digits: ( 7 = 1^3 + 2^3 ).
There are infinitely many prime numbers.
Further Reading
To learn more about number theory, you can read the following tutorials on our website: