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In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
Where a power of ten has different names in the two conventions, the long scale name is shown in parentheses. The positive 10 power related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10 [(prefix-number + 1) × 3] Examples: billion = 10 [(2 + 1) × 3] = 10 9; octillion = 10 [(8 + 1) × 3 ...
For instance, consider division by the regular number 54 = 2 1 3 3. 54 is a divisor of 60 3, and 60 3 /54 = 4000, so dividing by 54 in sexagesimal can be accomplished by multiplying by 4000 and shifting three places. In sexagesimal 4000 = 1×3600 + 6×60 + 40×1, or (as listed by Joyce) 1:6:40.
If a right triangle has integer side lengths a, b, c (necessarily satisfying the Pythagorean theorem a 2 + b 2 = c 2), then (a,b,c) is known as a Pythagorean triple. As Martin (1875) describes, the Pell numbers can be used to form Pythagorean triples in which a and b are one unit apart, corresponding to right triangles that are nearly isosceles.
A simple recurrence formula to generate trigonometric tables is based on Euler's formula and the relation: (+) = This leads to the following recurrence to compute trigonometric values s n and c n as above: c 0 = 1 s 0 = 0 c n+1 = w r c n − w i s n s n+1 = w i c n + w r s n