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Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of “to the power of 4”. The sequence of fourth powers of integers, known as biquadrates or tesseractic numbers, is:
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
The fourth power of the norm of a quaternion is the determinant of the corresponding matrix. The scalar part of a quaternion is one quarter of the matrix trace ...
As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system.Each radix four, eight, and sixteen is a power of two, so the conversion to and from binary is implemented by matching each digit with two, three, or four binary digits, or bits.
An n th root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x: r n = x . {\displaystyle r^{n}=x.} Every positive real number x has a single positive n th root, called the principal n th root , which is written x n {\displaystyle {\sqrt[{n}]{x}}} .
Numbers of the form 31·16 n always require 16 fourth powers. 68 578 904 422 is the last known number that requires 9 fifth powers (Integer sequence S001057, Tony D. Noe, Jul 04 2017), 617 597 724 is the last number less than 1.3 × 10 9 that requires 10 fifth powers, and 51 033 617 is the last number less than 1.3 × 10 9 that requires 11.
Allows for super-powers and super-exponential function by increasing the number of arrows; used in the article on large numbers. Text notation exp _ a ^ n(x) Based on standard notation; convenient for ASCII. J Notation x ^^: (n-1) x: Repeats the exponentiation. See J (programming language) [7] Infinity barrier notation
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...