Usage

There are two modules, numbers and primes.

Numbers

Find the greatest common divisor of the arguments.

The greatest common divisor of a and 0 is always a, as this coincides with gcd to be the greatest lower bound in the lattice of divisibility.

Find the least common multiple of the arguments.

The least common multiple of a and 0 is always 0, as this coincides with lcm to be the least upper bound in the lattice of divisibility.

Find the largest integer whose square is less than n.

Find the modular inverse of n modulo mod.

In python 3.6 and 3.7, the algorithm is based on using the Extended Euclid Algorithm, to solve the diophantine equation n*x + mod*y = 1.

In later versions this is just a wrapper over the pow function.

Return the nth Fibonacci number.

n can be a negative integer as well.

Make an iterator that returns the Fibonacci numbers.

The Fibonacci sequence is configurable, in the sense that the two initial values of it can be passed as arguments.

Calculate n choose k.

Calculation is using the multiplicative formula, and is performed from the side that will minimise the number of calculations.

Calculate the n-th s-gonal number.

Primes

Make an iterator that returns the primes up to upper_bound

This method uses the sieve of Eratosthenes to return the primes.

Check if n is a prime number.

This is a deterministic primality test, but it relies on GHR. This seems a good enough compromise. It is very fast for up to 81-bit integers, after which it is starts slowing down, due to the fact that we need to check for all possible Miller-Rabin witnesses.

Get the smallest prime that is larger than n.

Make an iterator that returns the prime numbers in ascending order.

Calculate the sum of the xth powers of the positive divisors of n