Wolfram|Alpha Mathematics

Number Theory

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)