In number theory, a perfect digital invariant (PDI) is a number in a given number base ( b {\displaystyle b} ) that is the sum of its own digits each...

(also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus perfect number) in a given number base...

{\displaystyle b} that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy numbers...

Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Sorting algorithm Hanover 2017...

Arithmetic dynamics Casting out nines Checksum Digital root Hamming weight Harshad number Perfect digital invariant Sideways sum Smith number Sum-product number...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number...

The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing...

be a perfect number. More generally, no Fibonacci number other than 1 can be multiply perfect, and no ratio of two Fibonacci numbers can be perfect. With...

and the fundamental theorem of arithmetic, and shows how to construct a perfect number from a Mersenne prime. Another Greek invention, the Sieve of Eratosthenes...