Number Theory
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
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
generate Pascal's triangle
7 rows of Pascal's triangle
compute a polygonal number
5th hexagonal number
get information about a number-theoretic function
Euler phi
do computations with number-theoretic functions
phi(110)
find the continued fraction representation of a number
continued fraction sqrt(2)
find continued fraction representations of a function
continued fraction tan x
identify algebraic integers and units
Is 1/(1+sqrt(5)) an algebraic integer?
find the minimal polynomial of an algebraic number