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The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
A positive divisor of that is different from is called a proper divisor or an aliquot part of (for example, the proper divisors of 6 are 1, 2, and 3). A number that does not evenly divide n {\displaystyle n} but leaves a remainder is sometimes called an aliquant part of n . {\displaystyle n.}
In the division of 43 by 5, we have: 43 = 8 × 5 + 3, so 3 is the least positive remainder. We also have that: 43 = 9 × 5 − 2, and −2 is the least absolute remainder. These definitions are also valid if d is negative, for example, in the division of 43 by −5, 43 = (−8) × (−5) + 3, and 3 is the least positive remainder, while,
Number fields are often studied as extensions of smaller number fields: a field L is said to be an extension of a field K if L contains K. (For example, the complex numbers C are an extension of the reals R, and the reals R are an extension of the rationals Q.) Classifying the possible extensions of a given number field is a difficult and ...
In chemistry, the last digit of the CAS registry number (a unique identifying number for each chemical compound) is a check digit, which is calculated by taking the last digit of the first two parts of the CAS registry number times 1, the previous digit times 2, the previous digit times 3 etc., adding all these up and computing the sum modulo 10.
The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts. The number q(n) is also equal to the number of partitions of n in which only odd summands are permitted. [20]
6 is the 2nd superior highly composite number, [5] the 2nd colossally abundant number, [6] the 3rd triangular number, [7] the 4th highly composite number, [8] a pronic number, [9] a congruent number, [10] a harmonic divisor number, [11] and a semiprime. [12] 6 is also the first Granville number, or -perfect number. A Golomb ruler of length 6 is ...
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