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8
Introduction
hoursofclassesaweek).Wehopethatourbookwillbeusefulforthelisten-
ersofintroductorylecturesdevotedtonumbertheory,sparingthemthetime
offindingthenecessaryfactsinthevastandsometimesnotveryaccessible
oreasilyreadableliterature.
Inprinciple,thematerialofthisbookdoesnotgobeyondthe19th
centurymathematics.Innocase,doweclaimanyoriginalityoftheresults
presented.Forthemostpart,theresultsarewell-known,andsogivingthe
exactsourcesdoesnotseemnecessary;weindicatethemonlyexceptionally.
Severalfragmentsofthebookwereinfluencedbywell-knownnumbertheory
monographs,including[4],[7],[10],[11];thisisoftenindicatedinthetext
atappropriateplaces.
Theonlyoriginalelementofthisbookisthechoiceandarrangement
ofthematerial;theauthorshopethatitwillhelprealizethetargetsof
introductorynumbertheorylectures,assetoutatthebeginningofthis
introduction.
Thebeautyofnumbertheoryliesinthefactthatontheonehandit
enrichesotherdomainsofmathematics,andontheotherhanditmakesfre-
quentuseoftheirmethodsandresults.Itwasourintentiontoemphasize
thesetwoaspectsandnottolimittheproblemsormethodspresentedto
thosetraditionallyattributedtonumbertheory.Itisourviewthatallfacts
andmethodselaboratedinotherareasofmathematicsareallowedinanum-
bertheorycourse.Thiscausescertainproblemsindeterminingthenecessary
prerequisitesthereadershouldknow.Thesecertainlyincludesomealgebra
background(elementsofthetheoryofringsandmodules)andelementsof
calculus(realandcomplexseries).
Eachchapteriscomplementedwithproblems,ofdifferentcomplexity.
Somesolutionsandhintsaregivenattheendofthebook.Thefragments
setinsmallertypemaybeomittedonfirstreading.
TheauthorsareverymuchindebtedtoJerzyTrzeciakforcarefullyread-
ingthemanuscriptandforhishelpfulremarksandsuggestions.
AndrzejBiałynicki-Birula
MariuszSkałba