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The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
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Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
Prince Rupert's cube. In geometry, Prince Rupert's cube is the largest cube that can pass through a hole cut through a unit cube without splitting it into separate pieces. Its side length is approximately 1.06, 6% larger than the side length 1 of the unit cube through which it passes. The problem of finding the largest square that lies entirely ...
Mela Merwoman, one of the protagonists of The Color of Her Panties, was introduced in Heaven Cent attempting to trick Prince Dolph into marrying her. Still desperate for a husband, Mela goes to ask the Good Magician Humfrey to find her a suitable mate. On the way, she joins forces with a civilized ogre named Okra and a positive young woman ...
Hypercube internetwork topology. In computer networking, hypercube networks are a type of network topology used to connect and route data between multiple processing units or computers. Hypercube networks consist of 2m nodes, which form the vertices of squares to create an internetwork connection. A hypercube is basically a multidimensional ...
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It is asserted in the motivations (first paragraph of Section motivation that Chebyshev cube root behaves better than cubic root. It is a unfounded and non neutral original research, as, for each asserted inconvenience of the cubic root function one may provide a similar inconvenience of the Chebyshev cubic root , as it is defined in the page ...