Search results
Results From The WOW.Com Content Network
Arrange the digits 1 to 9 in order so that the first two digits form a multiple of 2, the first three digits form a multiple of 3, the first four digits form a multiple of 4 etc. and finally the entire number is a multiple of 9.
Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [ 1 ] For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 ...
From the numbers listed in the table, it would seem that all self-descriptive numbers have digit sums equal to their base, and that they're multiples of that base. The first fact follows trivially from the fact that the digit sum equals the total number of digits, which is equal to the base, from the definition of self-descriptive number.
Furthermore, it is clear that even-digits with greater than or equal to 8, [10] and with 9 digits, [11] or odd-digits with greater than or equal to 15 digits [12] have multiple solutions. Although 11-digit and 13-digit numbers have only one solution, it forms a loop of five numbers and a loop of two numbers, respectively. [ 13 ]
If doubling a digit results in a value > 9, subtract 9 from it (or sum its digits). Sum all the resulting digits (including the ones that were not doubled). The check digit is calculated by (()), where s is the sum from step 3. This is the smallest number (possibly zero) that must be added to to make a multiple of 10.
The computer may also offer facilities for splitting a product into a digit and carry without requiring the two operations of mod and div as in the example, and nearly all arithmetic units provide a carry flag which can be exploited in multiple-precision addition and subtraction. This sort of detail is the grist of machine-code programmers, and ...
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.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.