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) 3 and (3 2) 3, respectively) and as squares ((2 3) 2 and (3 3) 2, respectively) In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n 6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its ...
The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048. [12] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits.
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 Erdős–Moser equation, + + + = (+) where m and k are positive integers, is conjectured to have no solutions other than 1 1 + 2 1 = 3 1. The sums of three cubes cannot equal 4 or 5 modulo 9, but it is unknown whether all remaining integers can be expressed in this form.
To determine a number in the table, take the number immediately to the left, then look up the required number in the previous row, at the position given by the number just taken. Values of 10 ↑ n b {\displaystyle 10\uparrow ^{n}b} = H n + 2 ( 10 , b ) {\displaystyle H_{n+2}(10,b)} = 10 [ n + 2 ] b {\displaystyle 10[n+2]b} = 10 → b → n
The number e (e = 2.71828...), also known as Euler's number, which occurs widely in mathematical analysis The number i , the imaginary unit such that i 2 = − 1 {\displaystyle i^{2}=-1} The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.
In 2017, it was proven [15] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
In arithmetic and algebra, the seventh power of a number n is the result of multiplying seven instances of n together. So: n 7 = n × n × n × n × n × n × n. Seventh powers are also formed by multiplying a number by its sixth power, the square of a number by its fifth power, or the cube of a number by its fourth power.