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In mathematics, a primitive root may mean: Primitive root modulo n in modular arithmetic; Primitive nth root of unity amongst the solutions of z n = 1 in a field; See ...
The Las Capas site near Tucson features the earliest irrigation system, dating to 1200 BCE, found in North America. The network of canals and small fields, each about 250 sq ft (23 m 2) in size, covers more than 100 acres (40 hectares) indicating a sizable community of people with the organization to undertake substantial public works project. [19]
Such an element is called a primitive λ-root modulo n. The Carmichael function is named after the American mathematician Robert Carmichael who defined it in 1910. [ 1 ] It is also known as Carmichael's λ function , the reduced totient function , and the least universal exponent function .
The final resolution came in the Homestead Law of 1862, with a moderated pace that gave settlers 160 acres free after they worked on it for five years. [17] From the 1770s to the 1830s, pioneers moved into the new lands that stretched from Kentucky to Alabama to Texas. Most were farmers who moved in family groups. [18]
According to geographer Michael Williams, by 1860, about 153 million acres of forest had been cleared for farms, and another 11 million acres cut down by industrial logging, mining, railroad construction, and urban expansion. A fourth of the original forest cover in the eastern states was gone.
Brace root development has been proposed to be a juvenile trait [24] because brace root emergence is halted once the plant reaches maturity. [6] [25] As plants transition from juvenile to adult, the adult nodes favor development of reproductive structures like ears, over brace roots. The relationship between juvenile-to-adult transition and ...
By the Late Devonian, forests of large, primitive plants existed: lycophytes, sphenophytes, ferns, and progymnosperms had evolved. Most of these plants have true roots and leaves, and many were quite tall. The tree-like Archaeopteris, ancestral to the gymnosperms, and the giant cladoxylopsid trees had true wood. These are the oldest known trees ...
If g is a primitive root modulo p, then g is also a primitive root modulo all powers p k unless g p −1 ≡ 1 (mod p 2); in that case, g + p is. [14] If g is a primitive root modulo p k, then g is also a primitive root modulo all smaller powers of p. If g is a primitive root modulo p k, then either g or g + p k (whichever one is odd) is a ...