Teorías de Números

 

3. Fl sgkugfetf fhfrigigm fstã rflcigmec`m ime lc gslc `f lms icjcllfrms y vgllcems gevfetc`c pmr Ydullyce, `me`f lms icjcllfrms sgfdprf `gife lc vfr`c` y lms vgllcems sgfdprf dgfetfe. Vec pfrsmec sf feiufetrc c `ms pfrsmecs, C y J8 ◍ C `gif “Cl dfems uem `f emsmtrms fs ue vgllcem— y J em `gif ec`c. ◍ C `gif “Lms `ms smdms icjcllfrms— y J `gif “C fs ue vgllcem—. ◍ Pcetm C imdm J `gife “Wm smy ue icjcllfrm—. ◍ @ftfrdgef sg fs pmsgjlf, quç sme C y J fe ic`c icsm. Yg em puf`f `ftfrdgecr quç sme, ½puf`fs `f`uigr clkuec imeilusgùe= Imeifpigùe

:. @fdufstrf quf (~) ∫ (~)  ~ ( ∢ ) sme lùkgicdfetf fqugvclfetfs.

9. _frgogquf sg fs tcutmlmkäc m em lms sgkugfetfs feueigc`ms8 c) ( ∫ ) ↚ ( ∢ )  j)  ↚ ( ∢ )

0. @f lcs prfdgscs `c`cs mjtfefdms quf ^f`rm sg fs cludem `f icliulm Yfce lcs prmpmsgigmefs8

p8 Zmsc tgfef 3; cóms q8 ^f`rm fs cludem `f iãliulm iã liulm w8 Ycdufl fs cludem `f lùkgic

 

x8 Pmdcs fs cludem `f iãliulm y8 Lugsc y Dcräc sme cludems `f kfmdfträc

Pfefdms quf8 Yg Zmsc tgfef 3; cóms, fetmeifs ^f`rm fs cludem `f iãliulm8  p ⇚ q ¬q ⇚ ¬p (efkce`m egfkm)

Zmsc tgfef 3; cóms y Ycdufl fs cludem `f lùkgic, m Pmdcs fs cludem `f iãliulm. (p∫w) ∢x (sf iudplf `f lcs `ms) Yg Pmdcs fs cludem `f iãliulm, fetmeifs Lugsc m Dcräc sme cludems `f Kfmdfträc. x ⇚ y ¬y ⇚ ¬x (efkce`m egfkm)

Pfefdms quf Lugsc eg Dcräc sme cludems `f Kfmdfträc8 fs `figr quf iudplf ¬y pmr lm tcetm sf iudplf ¬x, imdm8 (p∫w) ∢x y tcdjgçe ¬x sf iudplf p∫w y sg sf iudplf p fetmeifs sf iudplf q8 pmr lm tcetm, ^f`rm sg fs cludem `f iãliulm.

6. Ãekfl, Jmrgs, Içscr y @gfkm sf sfetcrme c jfjfr. Fl quf sf sfetù c lc gzqugfr`c `f Jmrgs, jfjgù ckuc. Ãekfl fstcjc orfetf cl quf jfjäc vgem. Sugfe sf sfetcjc c lc `frfibc `f @gfkm jfjäc ceäs. Fl `fl icoç y fl `fl ceäs fstcjce orfetf c orfetf. ½Iuãl frc lc jfjg`c `f ic`c bmdjrf= Icoç Jmrgs

 



Jmrgs- icoç



Ãekfl - ckuc



Içscr - ceäs



@gfkm - vgem _gem

Ckuc

@gfkm

Ãekfl

Ifscr  Ceäs

. ?. Imesg`frf lms imehuetms `gjuhc`ms fe fl krãogim y c`fdãs scjgfe`m quf8 # (  ∨ ) 4 :6, # (   √ ) 4 33, # (  ∧ ) 4 7, # ( √ ) 4 3:, # (  √ ) 4 ?

Pfegfe`m fe iufetc quf # fs lc icr`geclg`c` `fl imehuetm. @ftfrdgef lc

   

 

icr`geclg`c` `f lms imehuetms C, J, I.

;. Fe uec feiufstc rfclgzc`c c 3>> fstu`gcetfs sf feimetrù quf8 03 fstu`gcetfs

bcjlce fspcóml, :7 bcjlce orceiçs y :? bcjlce rusm. 36 fstu`gcetfs bcjlce fspcóml y orceiçs1 2 fstu`gcetfs bcjlce orceiçs y rusm1 37 fstu`gcetfs bcjlce fspcóml y rusm. C`fdãs 6 fstu`gcetfs bcjlce lcs trfs lfekucs. @ftfrdgecr8 c)

fl eødfrm `f fstu`gcetfs quf em bcjlc egekuec `f lcs trfs lfekucs, Z/ 03 pfrsmecs em bcjlce egekøe g`gmdc

j)

fl eødfrm `f fstu`gcetfs quf bcjlce smlcdfetf uec `f lcs lfekucs, Z/ :; fstu`gcetfs bcjlce smlcdfetf uec lfekuc.

i)

fl eødfrm `f fstu`gcetfs quf bcjlce orceiçs, pfrm em fspcóml. Z/ 39 fstu`gcetfs bcjlce orceiçs, pfrm em fspcóml.

 

3:

33

3>  

30

6 9

 0

03

 

2. Vec dãqugec imstù gegigcldfetf 3>02> `ùlcrfs. Cl icjm `f uems cóms sf

vfe`gù c lc dgtc` `f su prfigm. ^csc`ms uems cóms, vmlvgù c vfe`frsf pmr lc dgtc`, y csä suifsgvcdfetf. C ½Iuãetm lf imstù lc dãqugec cl qugetm prmpgftcrgm=

J ½Yg fl tmtcl `f prmpgftcrgms bc sg`m ;, ½iuãl fs lc sudc tmtcl pckc`c pmr fsc dãqugec= Fs uec prmkrfsgùe kfmdçtrgic ime 3>02> y r 4 0

c ½ c 64c3 . r 43>02>.

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j ½ c ;4c3 . r 43>02>.

() 3

0

:

3

43>02>

?

43>02>

()

c; . r c3 r √3

4

 3

3 3?9,;6. √3>02> : 3 :

√3

4

3?

?0

:

Y;4

 3

3>02> 3?

4

3>02>

3 :

4??6 furms

43?9,;6 furms

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4:>;7?,:6 furms