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The binary digital sum is crucial for the theory of the game of Nim. The digital sum in base b is an associative and commutative operation on the natural numbers; it has 0 as neutral element and every natural number has an inverse element under this operation. The natural numbers together with the base-b digital sum thus form an abelian group ...
The digit sum - add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13. The digital root - repeatedly apply the digit sum operation to the representation of a number in a given base until the outcome is a single digit. For example, considering ...
In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
implying a finite number of Dudeney roots and Dudeney numbers for each order and base . [2], is the digit sum. The only Dudeney numbers are the single-digit numbers in base , and there are no periodic points with prime period greater than 1.
The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit. The decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value.
The type-generic macros that correspond to a function that is defined for only real numbers encapsulates a total of 3 different functions: float, double and long double variants of the function. The C++ language includes native support for function overloading and thus does not provide the <tgmath.h> header even as a compatibility feature.
All numbers whose base b digit sum divides b−1 are harshad numbers in base b. For a prime number to also be a harshad number it must be less than or equal to the base number, otherwise the digits of the prime will add up to a number that is more than 1, but less than the prime, and will not be divisible.
A negative base (or negative radix) may be used to construct a non-standard positional numeral system.Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).