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All but finitely many positive integers can be expressed more simply as the sum of at most 46 seventh powers. [3] If powers of negative integers are allowed, only 12 powers are required. [4] The smallest number that can be represented in two different ways as a sum of four positive seventh powers is 2056364173794800. [5] The smallest seventh ...
The n th roots of unity allow expressing all n th roots of a complex number z as the n products of a given n th roots of z with a n th root of unity. Geometrically, the n th roots of unity lie on the unit circle of the complex plane at the vertices of a regular n -gon with one vertex on the real number 1.
The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.. An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients.
For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.
Every prime power (except powers of 2 greater than 4) has a primitive root; thus the multiplicative group of integers modulo p n (that is, the group of units of the ring Z/p n Z) is cyclic. [ 1 ] The number of elements of a finite field is always a prime power and conversely, every prime power occurs as the number of elements in some finite ...
Macy's has named 66 of the 150 stores that it's planning to close as part of its revitalization plan.. The retailer announced back in February 2024 plans to shut down 150 "underproductive" Macy's ...
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