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Then the triangle is in Euclidean space if the sum of the reciprocals of p, q, and r equals 1, spherical space if that sum is greater than 1, and hyperbolic space if the sum is less than 1. A harmonic divisor number is a positive integer whose divisors have a harmonic mean that is an integer. The first five of these are 1, 6, 28, 140, and 270.
In it, uniform blocks are stacked on top of each other to achieve the maximum sideways or lateral distance covered. The blocks are stacked 1/2, 1/4, 1/6, 1/8, 1/10, … distance sideways below the original block. This ensures that the center of gravity is just at the center of the structure so that it does not collapse.
The value of n is then the period of the decimal expansion of 1/p. [10] At present, more than fifty decimal unique primes or probable primes are known. However, there are only twenty-three unique primes below 10 100. The decimal unique primes are 3, 11, 37, 101, 9091, 9901, 333667, 909091, ... (sequence A040017 in the OEIS).
For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
This is one-half of the harmonic mean of 6 and 4: 2·6·4 / 6 + 4 = 4.8. That is, the appropriate average for the two types of pump is the harmonic mean, and with one pair of pumps (two pumps), it takes half this harmonic mean time, while with two pairs of pumps (four pumps) it would take a quarter of this harmonic mean time.
For a positive integer x, let M x denote the set of those n in {1, 2, ..., x} which are not divisible by any prime greater than p k (or equivalently all n ≤ x which are a product of powers of primes p i ≤ p k). We will now derive an upper and a lower estimate for | M x |, the number of elements in M x.
This result can be deduced from Fermat's little theorem, which states that 10 p−1 ≡ 1 (mod p). The base-10 digital root of the repetend of the reciprocal of any prime number greater than 5 is 9. [9] If the repetend length of 1 / p for prime p is equal to p − 1 then the repetend, expressed as an integer, is called a cyclic number.
10.1 Series representations. ... the reciprocal of the solution to ... The zeta function is defined for any complex number s with real part greater than 1 by the ...