Mathematics
# 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
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Diophantine Equations

solve a Diophantine equation

solve 3x+4y=5 over the integers
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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
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
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

minimal polynomial sqrt(2)+sqrt(3)