Search results
Results from the WOW.Com Content Network
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m , for which n / m is again an integer (which is necessarily also a divisor of n ). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21).
Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...
The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.
These twenty fractions are all the positive k / d ≤ 1 whose denominators are the divisors d = 1, 2, 4, 5, 10, 20. The fractions with 20 as denominator are those with numerators relatively prime to 20, namely 1 / 20 , 3 / 20 , 7 / 20 , 9 / 20 , 11 / 20 , 13 / 20 , 17 / 20 , 19 / 20 ...
For a squarefree semiprime = (with ) the value of Euler's totient function (the number of positive integers less than or equal to that are relatively prime to ) takes the simple form = () = (+) + This calculation is an important part of the application of semiprimes in the RSA cryptosystem . [ 7 ]
The Möbius function is defined by [3] = {= >The Möbius function can alternatively be represented as = () (),where is the Kronecker delta, () is the Liouville function, is the number of distinct prime divisors of , and () is the number of prime factors of , counted with multiplicity.
In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and = () whenever a and b are coprime.. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.
For every positive integer n, the set of the integers modulo n that are relatively prime to n is written as (Z/nZ) ×; it forms a group under the operation of multiplication. This group is not always cyclic, but is so whenever n is 1, 2, 4, a power of an odd prime, or twice a power of an odd prime (sequence A033948 in the OEIS).