Primes, divisibility, modular arithmetic
Recursively finds the greatest common divisor.
a and b have the same remainder when divided by m.
Holds when p is prime and gcd(a,p)=1.
Counts integers up to n coprime to n.
Approximates the number of primes below x.
Least common multiple via the greatest common divisor.
Closed form for the sum of the first n natural numbers.
Closed form for the sum of the first n squares.
A number is divisible by 3 if the sum of its digits is.
A number is divisible by 9 if the sum of its digits is.
Every integer is either even or odd.
The sum of the first n cubes equals the square of the sum.
Count of divisors from prime factorization exponents.
Sum of all divisors from prime factorization.
Euclid-Euler form of even perfect numbers.
Numbers one less than a power of two.
Numbers of a special exponential form.
Sum of the first n natural numbers.
The nth perfect square.
The nth pentagonal figurate number.
Each term is the sum of the two before it.
Closed form for the nth Fibonacci number.
Ratio where the whole is to the larger as the larger is to the smaller.
The rule of the famous unsolved Collatz conjecture.
A primality criterion for p.