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In number theory, the multiplicative digital root of a natural number in a given number base is found by multiplying the digits of together, then repeating this operation until only a single-digit remains, which is called the multiplicative digital root of .[1][2]
The multiplicative digital root for the first few positive integers are:
single-digit remains, which is called the multiplicativedigitalroot of n {\displaystyle n} . The multiplicativedigitalroot for the first few positive integers...
The digitalroot (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing...
each nonzero natural number n; the rational numbers, by including a multiplicative inverse 1 / n {\displaystyle 1/n} for each nonzero integer n (and also...
includes as a subproblem a special instance of the problem of finding the multiplicative order of a modular integer or of an element in a finite field. However...
prime power (except powers of 2 greater than 4) has a primitive root; thus the multiplicative group of integers modulo pn (that is, the group of units of...
invertible elements in a multiplicative monoid, that is, an algebraic structure, with an associative multiplication and a multiplicative identity denoted 1...
is the smallest number of multiplicative persistence 3. In base 10, there is thought to be no number with a multiplicative persistence > 11: this is known...
decimal digitalroot of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value. Digit sums and digital roots...
from the multiplicative group of the field to a totally ordered additive group, also called orders), absolute values (certain multiplicative mappings...
by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digitalroot of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every...
a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples...
{\displaystyle b} that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy...
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus...
until a single digit (called the digitalroot) is obtained, always produces the number 1. For example, the digitalroot of 8128 is 1, because 8 + 1 + 2...
4.[dubious – discuss] By analogy with the cube root of x, one can define the (real) tetrahedral root of x as the number n such that Ten = x: n = 3 x...
terms in this formula are multiplicative but not completely multiplicative. Therefore, the harmonic mean H(n) is also multiplicative. This means that, for...
8437, 8893, 9361, 9841, 10333, 10837 (sequence A003154 in the OEIS) The digitalroot of a star number is always 1 or 4, and progresses in the sequence 1,...
→ 0 c ( x ) = 1 {\displaystyle C_{0}=\lim _{x\to 0}c(x)=1} . The square root term can be expanded as a power series using the binomial series 1 − 1 −...
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