Number theory is a branch of mathematics dealing with whole numbers and their properties. Prime numbers, divisors and Diophantine equations, among others, are important related concepts. Applications of modern number theory are numerous, including topics that range from elliptic-curve cryptography to music theory.
Primes are the building blocks of the naturals. Compute prime factorizations, find nth primes or make lists of primes.
Solve equations with one or many unknowns, considering only integer solutions.
Find the most specific number type that encompasses all possible outputs from an expression involving general number types.
Test if a number divides another, compute a number's divisors or find the greatest common divisor for a set of numbers.
Convert numbers between bases and compute the sum of their digits.
Compute the finite or infinite continued fraction representations of numbers and functions.
Step-by-Step Solutions for Discrete Mathematics
Work with notable integers and classes of integers, such as the polygonal numbers and the binomial coefficients.