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On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared is odd) modulo 4.
Prairie ecosystems in the United States and Canada are divided into the easternmost tallgrass prairie, the westernmost shortgrass prairie, and the central mixed-grass prairie. Tallgrass prairies receive over 30 inches of rainfall per year, whereas shortgrass prairies are much more arid, receiving only 12 inches or so, and mixed-grass prairies ...
The frontispiece and title page of Commerce of the Prairies A Map of the Indian Territory, published in Commerce of the Prairies. Gregg's book Commerce of the Prairies, published in two volumes in 1844, is an account of his time spent as a trader on the Santa Fe Trail from 1831 to 1840 and includes commentary on the geography, botany, geology, and culture of New Mexico. [6]
The North America Prairies is a large grassland floristic province within the North American Atlantic Region, a floristic region within the Holarctic Kingdom. It lies between the Appalachian Province and the Rocky Mountains and includes the prairies of the Great Plains .
The sum of one odd square and one even square is congruent to 1 mod 4, but there exist composite numbers such as 21 that are 1 mod 4 and yet cannot be represented as sums of two squares. Fermat's theorem on sums of two squares states that the prime numbers that can be represented as sums of two squares are exactly 2 and the odd primes congruent ...
Picturesque America was a two-volume set of books describing and illustrating the scenery of America, which grew out of an earlier series in Appleton's Journal.It was published by D. Appleton and Company of New York in 1872 and 1874 and edited by the romantic poet and journalist William Cullen Bryant (1794–1878), who also edited the New York Evening Post.
Anaphora is the repetition of a word, phrase, or clause at the beginning of word groups occurring one after the other. Examples: (1) Give me wine, give me women and give me song. (2) For everything there is a season . . . a time to be born, and a time to die; a time to plant, and a time to pluck up what is planted.—Bible, Ecclesiastes.
Robert H. Birch with his Banditti outlaw partners, William Fox and John Long burying ill-gotten loot An illustration of Edward Bonney, from his book Banditti of the Prairies who as a bounty hunter and amateur detective in 1846, began a man-hunt doggedly pursued Robert Birch and his accomplices in the "Banditti of the Prairie", from Illinois to ...