By David Burton
Common quantity idea, 7th variation, is written for the one-semester undergraduate quantity concept direction taken through math majors, secondary schooling majors, and laptop technological know-how scholars. this modern textual content offers an easy account of classical quantity concept, set opposed to a old heritage that exhibits the subject's evolution from antiquity to contemporary examine. Written in David Burton’s enticing type, straight forward quantity conception finds the charm that has drawn top mathematicians and amateurs alike to quantity thought over the process historical past.
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Extra info for Elementary Number Theory (7th Edition)
An . Corollary 2. If p, qi, q2, ... , qn are all primes and p I qiq2 · · · qn, then p = qk for some k, where 1 :::; k:::; n. Proof. By virtue of Corollary 1, we know that p I qk for some k, with 1 :::; k:::; n. Being a prime, qk is not divisible by any positive integer other than 1 or qk itself. Because p > 1, we are forced to conclude that p = qk. With this preparation out of the way, we arrive at one of the cornerstones of our development, the Fundamental Theorem of Arithmetic. 2. · 2 · 3 2 is 3.
7. When Mr. Smith cashed a check at his bank, the teller mistook the number of cents for the number of dollars and vice versa. Unaware of this, Mr. Smith spent 68 cents and then noticed to his surprise that he had twice the amount of the original check. Determine the smallest value for which the check could have been written. ] 8. Solve each of the puzzle-problems below: (a) Alcuin of York, 775. One hundred bushels of grain are distributed among 100 persons in such a way that each man receives 3 bushels, each woman 2 bushels, and each child !
Smith spent 68 cents and then noticed to his surprise that he had twice the amount of the original check. Determine the smallest value for which the check could have been written. ] 8. Solve each of the puzzle-problems below: (a) Alcuin of York, 775. One hundred bushels of grain are distributed among 100 persons in such a way that each man receives 3 bushels, each woman 2 bushels, and each child ! bushel. How many men, women, and children are there? (b) Mahaviracarya, 850. There were 63 equal piles of plantain fruit put together and 7 23 travelers.
Elementary Number Theory (7th Edition) by David Burton