Prime Numbers

compute a prime factorization

factor 70560

specify a prime by its position in the sequence 2, 3, 5, ...

1,000,000th prime

generate a list of primes

primes <= 100

Divisors

compute the divisors of an integer

divisors 3600

compute a greatest common divisor

gcd 24, 36, 48, 60

Diophantine Equations

solve a Diophantine equation

solve 3x+4y=5 over the integers

Digit Sums

sum the digits of an integer

add up the digits of 2567345

compute the digit sum in another base

sum of digits of 29225 in base 2

Special Numbers

compute a polygonal number

5th hexagonal number

determine whether a number belongs to a given class

Does the set of perfect numbers contain 18?

find numbers matching specified criteria

20 greatest triangular numbers < 500

generate Pascal's triangle

7 rows of Pascal's triangle

Number Theoretic Functions

get information about a number theoretic function

Euler phi

do computations with number theoretic functions

phi(110)

Continued Fractions

find the continued fraction representation of a number

continued fraction sqrt(2)

find continued fraction representations of a function

continued fraction tan x

Algebraic Numbers

identify algebraic integers and units

Is 1/(1+sqrt(5)) an algebraic integer?

find the minimal polynomial of an algebraic number

minimal polynomial sqrt(2)+sqrt(3)