Elementary Number Theory with Applications.pdf

Elementary Number Theory with Applications.pdf

ID:34406855

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时间:2019-03-05

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1、ListofSymbolsSymbolMeaningPageSymbolMeaningPageZsetofintegers(3)a

2、baisafactorofb(74)x∈SxbelongstosetS(3)abaisnotafactorofb(74)x∈/SxdoesnotbelongtosetS(3)

3、A

4、thenumberofelementsinsetA(76)Z+setofpositiveintegers(3)A∪BtheunionofsetsAandB(76)Nsetofpositiveintegers(3)A∩Btheintersectionofsets

5、AandB(76)Wsetofwholenumbers(4)AthecomplementofsetA(76)abaisgreaterthanb(4)Rnrepunitwithnones(96)a≤babora=b(5)FnthenthFibonaccinumber(129)min{x,y}theminimumofxandy(5)LnthenthLucasnu

6、mber(136)

7、A

8、thedeterminantofmatrixA(138)max{x,y}themaximumofxandy(5)fnthenthFermatnumber(139)

9、x

10、theabsolutevalueofx(5)(a,b)thegreatestcommonfactorofaandb(155)xtheflooroftherealnumberx(6)(a1,a2,...,an)thegreatestcommonfactorofa1,a2,...,andan(162)xtheceilingoftherealnumberx(6)i=mmmpanp

11、aexactlydividesn(183)ai=ai=aiak+ak+1+···+am(9)[a,b]theleastcommonmultipleofaandb(184)i=ki=kk[a1,a2,...,an]theleastcommonmultipleofa1,a2,...,andan(187)aithesumofthevaluesofaiasirunsoverthevariousvaluesinI(11)a≡b(modm)aiscongruenttobmodulom(212)i∈Ia≡b(modm)aisnotcongruenttobmodulom(2

12、12)aijthesumofthevaluesofaij,whereiandjsatisfypropertiesP(11)[r]thecongruenceclassrepresentedbyr(216)P−1aaninverseofamodulom(234)i=mmmai=ai=aiakak+1···am(13)ρ(n)thedigitalrootofn(291)i=ki=kkIntheidentitymatrixofordern(316)n!nfactorial(13)n#theproductofprimes≤n(325)nbinomialcoeffici

13、ent(33)ϕ(n)Euler’sphifunction(342)rτ(n)thenumberofpositivefactorsofn(365)tntriangularnumber(40)σ(n)thesumofthepositivefactorsofn(366)snsquarenumber(44)MpMersennenumber2p−1(381)pnpentagonalnumber(46)μ(n)Möbiusfunction(398)hnhexagonalnumber(48)λ(n)Liouvillefunction(405)Tntetrahedralnumber

14、(49)ordmatheorderofamodulom(456)Snsquarepyramidalnumber(50)ψ(d)thenumberofincongruentresiduesoforderdmodulop(470)Pnpentagonalpyramidalnumber(51)indαatheindexofatothebaseα(483)Hnhexagonalpyramidalnumber(51)(a/p)Legendresymbol(501)adivbthequotientwhenaisdividedbyb(71)(a/m)Jacobis

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