The one
In a multiplicative group or monoid , the identity element is sometimes denoted 1 , but e (from the German Einheit , "unity") is more traditional. However, 1 is especially common for the multiplicative identity of a ring, i.e., when an addition and 0 are also present. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n 1 = 1 n = 0 (where this 0 is the additive identity of the ring). Important examples are general fields .
Dollar
The dollar (often represented by the dollar sign $) is the name of the official currency of many countries, including the United States, Canada, the Eastern Caribbean territories, Ecuador, Suriname, El Salvador, Panama, Belize, Singapore, Hong Kong, Taiwan, Brunei, East Timor, Australia, and New Zealand.Lottery
Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. At the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes , were illegal in many countries, including the U.S.A. and most of Europe. This remained so until after World War II. In the 1960s casinos and lotteries began to appear throughout the world as a means to raise revenue in addition to taxes.Mind blow by math
In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number.
For a given natural number k, a number n is called k-perfect (or k-fold perfect) if and only if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and only if it is 2-perfect. A number that is k-perfect for a certain k is called a multiply perfect number. As of July 2004, k-perfect numbers are known for each value of k up to 11.
There are hints in the surviving records of the ancient Egyptians that they had some knowledge of prime numbers: the Egyptian fraction expansions in the Rhind papyrus, for instance, have quite different forms for primes and for composites. However, the earliest surviving records of the explicit study of prime numbers come from the Ancient Greeks. Euclid's Elements (circa 300 BC) contain important theorems about primes, including the infinitude of primes and the fundamental theorem of arithmetic. Euclid also showed how to construct a perfect number from a Mersenne prime. The Sieve of Eratosthenes, attributed to Eratosthenes, is a simple method to compute primes, although the large primes found today with computers are not generated this way.
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Various methods called primality tests determine whether a given number n is prime. Most such methods only tell whether n is prime or not but do not yield the prime factors of n. A routine accomplishing the latter task, too, is called a factorization algorithm.