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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 digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For example, in base 10, the digital root of the number 12345 is 6 because the sum of the digits in the number is 1 + 2 + 3 + 4 + 5 = 15, then the addition process is repeated again for the resulting number 15, so that the sum of 1 + 5 equals 6, which is the digital root of that number. In base 10, this is equivalent to taking the remainder upon division by 9 (except when the digital root is 9, where the remainder upon division by 9 will be 0), which allows it to be used as a divisibility rule.
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...
In number theory, the multiplicative digitalroot of a natural number n {\displaystyle n} in a given number base b {\displaystyle b} is found by multiplying...
84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13. The digitalroot - repeatedly apply the digit sum operation to the representation of a...
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...
digitalroot of 36 is 3 + 6 = 9. The sum of the digits of 35967930 is 3 + 5 + 9 + 6 + 7 + 9 + 3 + 0 = 42, and 35967930 − 42 = 35967888. The digital root...
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...
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...
number is called the "digitalroot" of the original. If a number is divisible by 9, its digitalroot is 9. Otherwise, its digitalroot is the remainder it...
typical 9 × 9 multiplication table where the entry in each cell is the digitalroot of the product of the column and row headings i.e. the remainder when...
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,...
make use of the representation of a number as a sequence of digits. The digitalroot is the single-digit number obtained by summing the digits of a given...
{\displaystyle b} that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy...
Eratosthenes can be sped up by considering only the prime divisors up to the square root of the upper limit. Fibonacci took the innovations from Islamic mathematics...
the fly. The digital certificate chain of trust starts with a self-signed certificate, called a root certificate, trust anchor, or trust root. A certificate...
rationals; the complex numbers, by adjoining to the real numbers a square root of −1 (and also the sums and products thereof); and so on. This chain of...
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...
which is a power of two and much smaller. Power of 10 Power of two Square root of 3 Ranucci, Ernest R. (December 1968), "Tantalizing ternary", The Arithmetic...
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus...
number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001...
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