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For example, to determine whether 913 = 10 × 91 + 3 is divisible by 11, find that m = (11 × 9 + 1) ÷ 10 = 10. Then mq + t = 10 × 3 + 91 = 121; this is divisible by 11 (with quotient 11), so 913 is also divisible by 11. As another example, to determine whether 689 = 10 × 68 + 9 is divisible by 53, find that m = (53 × 3 + 1
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
For example, there are six divisors of 4; they are 1, 2, 4, −1, −2, and −4, but only the positive ones (1, 2, and 4) would usually be mentioned. 1 and −1 divide (are divisors of) every integer. Every integer (and its negation) is a divisor of itself. Integers divisible by 2 are called even, and integers not divisible by 2 are called odd.
046 454 286 <--- A fictitious, but valid, SIN. 121 212 121 <--- Multiply every second digit by 2. The result of the multiplication is: 0 8 6 8 5 8 2 16 6 Then, add all of the digits together (note that 16 is summed as the individual digits 1+6): 0 + 8 + 6 + 8 + 5 + 8 + 2 + 1+6 + 6 = 50 If the SIN is valid, this number will be evenly divisible ...
37 is a prime number, [1] a sexy prime, and a Padovan prime 37 is the first irregular prime with irregularity index of 1. [2] 37 is the smallest non-supersingular prime in moonshine theory. 37 is also an emirp because it remains prime when its digits are reversed.
[1] The prime numbers are precisely the atoms of the division lattice, namely those natural numbers divisible only by themselves and 1. [2] For any square-free number n, its divisors form a Boolean algebra that is a sublattice of the division lattice. The elements of this sublattice are representable as the subsets of the set of prime factors ...
In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. [1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. [2] One says also a is prime to b or a ...
In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Greek mathematics ; the latter have become common in recent decades.