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Of the form a 2 n + 1 for fixed integer a. ... the k-th harmonic number and ω p denotes the Wolstenholme quotient. ... in the Pell number sequence P 0 = 0, P 1 = 1 ...
This thermometer is indicating a negative Fahrenheit temperature (−4 °F). In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency.
The characteristic of a ring is a non-negative integer generating the Z-ideal of multiples of 1 that are zero. clean 1. A finitely generated module M over a Noetherian ring R is called clean if it has a finite filtration all of whose quotients are of the form R/p for p an associated prime of M.
The IBM System/360, announced in 1964, was a popular computer system with 24-bit addressing and 32-bit general registers and arithmetic. The early 1980s saw the first popular personal computers, including the IBM PC/AT with an Intel 80286 processor using 24-bit addressing and 16-bit general registers and arithmetic, and the Apple Macintosh 128K with a Motorola 68000 processor featuring 24-bit ...
In mathematics, the notion of number has been extended over the centuries to include zero (0), [3] negative numbers, [4] rational numbers such as one half (), real numbers such as the square root of 2 and π, [5] and complex numbers [6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or ...
Let b be a positive integer greater than 1. Then every positive integer a can be expressed uniquely in the form = + + + +, where m is a nonnegative integer and the r's are integers such that 0 < r m < b and 0 ≤ r i < b for i = 0, 1, . . . , m − 1. [32]
Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1.
Given a Gaussian integer z 0, called a modulus, two Gaussian integers z 1,z 2 are congruent modulo z 0, if their difference is a multiple of z 0, that is if there exists a Gaussian integer q such that z 1 − z 2 = qz 0. In other words, two Gaussian integers are congruent modulo z 0, if their difference belongs to the ideal generated by z 0.