Invitation to Number Theory Øystein Ore

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129 pages


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Invitation to Number Theory  by  Øystein Ore

Invitation to Number Theory by Øystein Ore
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Number theory has been instrumental in introducing many of the most distinguished mathematicains, past and present, to the charms and mysteries of mathematical research. The purpose of this simple little guide will have been achieved if it shouldMoreNumber theory has been instrumental in introducing many of the most distinguished mathematicains, past and present, to the charms and mysteries of mathematical research.

The purpose of this simple little guide will have been achieved if it should lead some of its readers to appreciate why the properties of nubers can be so fascinating. It would be better still if it would induce you to try to find some number relations of your own- new curiosities devised by young people turn up every year. In any case, you will become familiar with some of the special mathematical concepts and methods used in number theory and will be prepared to embark upon the study of the more advanced books in its rich literature.Contents1. IntroductionHistoryNumerologyThe Pythagorean problemFigurate numbersMagic squares2.

PrimesPrimes and composite numbersMersenne primesFermat primesThe sieve of Eratosthenes3. Divisors of numbersFundamental factorization theoremDivisorsProblems concerning divisorsPerfect numbersAmicable numbers4. Greatest common divisor and least common multipleGreatest common divisorRelatively prime numbersEuclid´s algorithmLeast common multiple5.

The Pythagorean problemPreliminariesSolutions of the Pythagorean equationProblems connected with Pythagorea triangles6. Numeration systemsNumbers for the millionsOther systemsComparisons of numeration systemsSome problems concerning numeration systemsComputers and their numeration systemsGames with digits7. CongruencesDefinition of congruenceSome properties of congruencesThe algebra of congruencesPowers of congruencesFermat´s congruence8. Some applications of congruencesChecks on computationsThe days of the weekTournament schedulesPrime or composite?Solutions to selected problemsReferencesIndex



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