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Gauss proved [10] that for any prime number p (with the sole exception of p = 3), the product of its primitive roots is congruent to 1 modulo p. He also proved [11] that for any prime number p, the sum of its primitive roots is congruent to μ (p − 1) modulo p, where μ is the Möbius function. For example,
The Pan-American Highway is a system of roads measuring about 30,000 km (19,000 mi) [14] in length that runs north–south through the entirety of North, Central and South America, with the sole exception of a 106 km (66 mi) stretch of marshland and mountains between Panama and Colombia known as the Darién Gap.
In number theory, Artin's conjecture on primitive roots states that a given integer a that is neither a square number nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes. This conjectural density equals Artin's constant or a rational multiple thereof.
The following is an alphabetical list of Greek and Latin roots, stems, and prefixes commonly used in the English language from P to Z. See also the lists from A to G and from H to O . Some of those used in medicine and medical technology are not listed here but instead in the entry for List of medical roots, suffixes and prefixes .
The Gulf of Darién was the site of the Darien scheme, autonomous Scotland's one major attempt at colonialism. The first expedition of five ships (Saint Andrew, Caledonia, Unicorn, Dolphin, and Endeavour) set sail from Leith on July 14, 1698, with around 1,200 people on board. [6]
A&P. Perhaps one of the best-known defunct grocery store chains, A&P, or the Great Atlantic & Pacific Tea Company, traces its roots back to 1859, beginning as a mail-order tea business in New York ...
Thousands of hours of work can go into a red-carpet gown or royal wedding dress. But those efforts pale in comparison to elaborate beaded outfits made about 5,000 years ago in southwestern Spain.
While remaining independent and privately held, Cameron Mitchell Restaurants has grown to 50 restaurant locations across the country from Beverly Hills to New York City, and 20 different concepts in 15 states and the District of Columbia, including the steakhouse and seafood restaurant, Ocean Prime. Cameron Mitchell also runs a separate ...