[SPAM] [obm-l] Res: [obm-l] RES: [obm-l] Res: [obm-l] demonstração: pequeno teorema de FERMAT

[Rodrigo Cientista <rodrigocientista@xxxxxxxxxxxx>]

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Obrigado Artur, mas eu estava tentando mesmo era uma prova mais simples das=
 que eu conhe=E7o, s=F3 por distra=E7=E3o... conhe=E7o uma prova com fatori=
ais.=0A=0AValeu=0A=0A=0A----- Mensagem original ----=0ADe: Artur Costa Stei=
ner <artur.steiner@xxxxxxxxxx>=0APara: obm-l@xxxxxxxxxxxxxx=0AEnviadas: Seg=
unda-feira, 26 de Novembro de 2007 15:20:51=0AAssunto: [obm-l] RES: [obm-l]=
 Res: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT=0A=0A=0ANeste lim=
k h=E1 uma prova=0AArtur=0A-----Mensagem original-----=0ADe: owner-obm-l@ma=
t.puc-rio.br [mailto:owner-obm-l@xxxxxxxxxxxxxx]Em nome de Rodrigo Cientist=
a=0AEnviada em: segunda-feira, 26 de novembro de 2007 13:41=0APara: obm-l@m=
at.puc-rio.br=0AAssunto: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teo=
rema de FERMAT=0A=0A=0ASalhab, realmente houve uma falha=0A =0Ao teorema di=
z que n^p =3D=3Dn mod p, o que n=E3o sabemos...=0A =0Aseja x um resto qualq=
uer da divis=E3o de n por p, tal que n =3D=3D x mod p=0A =0Aseja um k qualq=
uer tal que x-k =3D 1 (chamarei de r) e n-k =3D w, assim n =3D=3D x mop p =
=E9 equivalente a n - k =3D=3D x - k mop p que pode ser reescrito como w =
=3D=3D r mod p =0A =0Aw =3D=3D r mod p implica w^p =3D=3D r^p mod p =0A =0A=
w^p -w =3D=3D r^p - r =3D=3D 0 mod p, assim w^p =3D=3D w =3D=3D 1 mod p (oq=
 s=F3 demonstra o teorema quando w deixa resto 1 na divis=E3o por p, tentei=
 provar por indu=E7=E3o para w+1, mas n=E3o saiu...)=0A=0A=0A =0A----- Mens=
agem original ----=0ADe: Marcelo Salhab Brogliato <msbrogli@xxxxxxxxx>=0APa=
ra: obm-l@xxxxxxxxxxxxxx=0AEnviadas: S=E1bado, 24 de Novembro de 2007 20:16=
:58=0AAssunto: Re: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT=0A=
=0AOl=E1 Rodrigo,=0A=0An=E3o entendi essa passagem: x^p - x =3D=3D n^p - n =
=3D=3D 0 mod p ...=0Ade onde veio o 0?=0A=0Aabra=E7os,=0ASalhab=0A=0A=0A=0A=
On Nov 24, 2007 6:01 PM, Rodrigo Cientista < rodrigocientista@xxxxxxxxxxxx>=
 wrote:=0A=0AEm primeiro lugar ol=E1 a todos, sou novo na lista, e gostaria=
 de saber se uma demonstra=E7=E3o que dei para o pequeno teorema de fermat =
est=E1 equivocada ou n=E3o, conforme segue: =0A=0Ao teorema diz que n^p =3D=
=3Dn mod p, o que n=E3o sabemos...=0A=0Aescreverei n =3D=3D x mod p, assim =
n =3D=3D x mod p implica n^p =3D=3D x^p mod p (das propriedades de congru=
=EAncia)=0A=0An^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p (das pro=
priedades de congru=EAncia) =0A=0Ase n =3D=3D x mod p e x^p =3D=3D n^p mod =
p ent=E3o n + x^p =3D=3D x+ n^p mod p (das propriedades de congru=EAncia)=
=0A=0Aassim x^p - x =3D=3D n^p - n =3D=3D 0 mod p implica n^p =3D=3D n mod =
p como quer=EDamos demonstrar=0A=0A=0A     Abra sua conta no Yahoo! Mail, o=
 =FAnico sem limite de espa=E7o para armazenamento! =0Ahttp://br.mail.yahoo=
.com/=0A=0A=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=0AInstru=E7=F5es para entrar na lista, sair da lista e usar a lista =
em =0Ahttp://www.mat.puc-rio.br/~obmlistas/obm-l.html=0A=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A=0A=0A=0A=0A=0A=0A=0A=
=0AAbra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para arm=
azenamento!=0A=0A=0A      Abra sua conta no Yahoo! Mail, o =FAnico sem limi=
te de espa=E7o para armazenamento!=0Ahttp://br.mail.yahoo.com/
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<html><head><style type=3D"text/css"><!-- DIV {margin:0px;} --></style></he=
ad><body><div style=3D"font-family:times new roman, new york, times, serif;=
font-size:12pt"><DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman=
, new york, times, serif">Obrigado Artur, mas eu estava tentando mesmo era =
uma prova mais simples das que eu conhe=E7o, s=F3 por distra=E7=E3o... conh=
e=E7o uma prova com fatoriais.</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-=
FAMILY: times new roman, new york, times, serif">&nbsp;</DIV>=0A<DIV style=
=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">=
Valeu<BR><BR></DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new=
 roman, new york, times, serif">----- Mensagem original ----<BR>De: Artur C=
osta Steiner &lt;artur.steiner@xxxxxxxxxx&gt;<BR>Para: obm-l@xxxxxxxxxxxxxx=
<BR>Enviadas: Segunda-feira, 26 de Novembro de 2007 15:20:51<BR>Assunto: [o=
bm-l] RES: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT=
<BR><BR>=0A<STYLE type=3Dtext/css>DIV {=0AMARGIN:0px;}=0A</STYLE>=0A=0A<DIV=
><SPAN class=3D919372017-26112007><FONT face=3DArial color=3D#0000ff size=
=3D2>Neste limk h=E1 uma prova</FONT></SPAN></DIV>=0A<DIV><SPAN class=3D919=
372017-26112007><FONT face=3DArial color=3D#0000ff size=3D2>Artur</FONT></S=
PAN></DIV>=0A<BLOCKQUOTE>=0A<DIV class=3DOutlookMessageHeader dir=3Dltr ali=
gn=3Dleft><FONT face=3DTahoma size=3D2>-----Mensagem original-----<BR><B>De=
:</B> owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx]<B>Em n=
ome de </B>Rodrigo Cientista<BR><B>Enviada em:</B> segunda-feira, 26 de nov=
embro de 2007 13:41<BR><B>Para:</B> obm-l@xxxxxxxxxxxxxx<BR><B>Assunto:</B>=
 [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT<BR><BR></=
FONT></DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, =
new york, times, serif">=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: time=
s new roman, new york, times, serif">Salhab, realmente houve uma falha</DIV=
>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: ti=
mes new roman, new york, times, serif">o teorema diz que n^p =3D=3Dn mod p,=
 o que n=E3o sabemos...</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY:=
 times new roman, new york, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT=
-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">seja&nbs=
p;x um resto qualquer da divis=E3o de n por p, tal que n =3D=3D x mod p</DI=
V>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york,=
 times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: t=
imes new roman, new york, times, serif">seja&nbsp;um k qualquer tal que x-k=
 =3D 1 (chamarei de r) e n-k =3D w, assim n =3D=3D x mop p =E9 equivalente =
a n - k =3D=3D x - k mop p que pode ser reescrito como w =3D=3D r mod p </D=
IV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york=
, times, serif">&nbsp;</DIV>=0A<P>w =3D=3D r mod p implica w^p =3D=3D r^p m=
od p </P>=0A<P>&nbsp;</P>=0A<P>w^p -w =3D=3D r^p - r =3D=3D 0 mod p, assim =
w^p =3D=3D w =3D=3D 1 mod p (oq s=F3 demonstra o teorema quando w deixa res=
to 1 na divis=E3o por p, tentei provar por indu=E7=E3o para w+1, mas n=E3o =
saiu...)</P>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman,=
 new york, times, serif"><BR><BR>&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12=
pt; FONT-FAMILY: times new roman, new york, times, serif">----- Mensagem or=
iginal ----<BR>De: Marcelo Salhab Brogliato &lt;msbrogli@xxxxxxxxx&gt;<BR>P=
ara: obm-l@xxxxxxxxxxxxxx<BR>Enviadas: S=E1bado, 24 de Novembro de 2007 20:=
16:58<BR>Assunto: Re: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT<B=
R><BR>Ol=E1 Rodrigo,<BR><BR>n=E3o entendi essa passagem: x^p - x =3D=3D n^p=
 - n =3D=3D 0 mod p ...<BR>de onde veio o 0?<BR><BR>abra=E7os,<BR>Salhab<BR=
><BR><BR>=0A<DIV class=3Dgmail_quote>On Nov 24, 2007 6:01 PM, Rodrigo Cient=
ista &lt;<A href=3D"mailto:rodrigocientista@xxxxxxxxxxxx"; target=3D_blank r=
el=3Dnofollow ymailto=3D"mailto:rodrigocientista@xxxxxxxxxxxx";> rodrigocien=
tista@xxxxxxxxxxxx</A>&gt; wrote:<BR>=0A<BLOCKQUOTE class=3Dgmail_quote sty=
le=3D"PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: rgb(204,20=
4,204) 1px solid">Em primeiro lugar ol=E1 a todos, sou novo na lista, e gos=
taria de saber se uma demonstra=E7=E3o que dei para o pequeno teorema de fe=
rmat est=E1 equivocada ou n=E3o, conforme segue: <BR><BR>o teorema diz que =
n^p =3D=3Dn mod p, o que n=E3o sabemos...<BR><BR>escreverei n =3D=3D x mod =
p, assim n =3D=3D x mod p implica n^p =3D=3D x^p mod p (das propriedades de=
 congru=EAncia)<BR><BR>n^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p=
 (das propriedades de congru=EAncia) <BR><BR>se n =3D=3D x mod p e x^p =3D=
=3D n^p mod p ent=E3o n + x^p =3D=3D x+ n^p mod p (das propriedades de cong=
ru=EAncia)<BR><BR>assim x^p - x =3D=3D n^p - n =3D=3D 0 mod p implica n^p =
=3D=3D n mod p como quer=EDamos demonstrar<BR><BR><BR>&nbsp; &nbsp; &nbsp;A=
bra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazen=
amento! <BR><A href=3D"http://br.mail.yahoo.com/"; target=3D_blank
 rel=3Dnofollow>http://br.mail.yahoo.com/</A><BR><BR>=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR>Instru=E7=F5es para ent=
rar na lista, sair da lista e usar a lista em <BR><A href=3D"http://www.mat=
.puc-rio.br/%7Eobmlistas/obm-l.html" target=3D_blank rel=3Dnofollow>http://=
www.mat.puc-rio.br/~obmlistas/obm-l.html</A><BR>=3D=3D=3D=3D=3D=3D=3D=3D=3D=
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=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<BR></BLOCKQUOTE></DIV><BR></DIV>=
=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, t=
imes, serif"><BR></DIV></DIV><BR>=0A<HR SIZE=3D1>=0AAbra sua conta no <A hr=
ef=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.com/"=
 target=3D_blank rel=3Dnofollow>Yahoo! Mail</A>, o =FAnico sem limite de es=
pa=E7o para armazenamento! </BLOCKQUOTE></DIV>=0A<DIV style=3D"FONT-SIZE: 1=
2pt; FONT-FAMILY: times new roman, new york, times, serif"><BR></DIV></div>=
<br>=0A=0A=0A      <hr size=3D1>Abra sua conta no <a href=3D"http://br.rd.y=
ahoo.com/mail/taglines/mail/*http://br.mail.yahoo.com/";>Yahoo! Mail</a>, o =
=FAnico sem limite de espa=E7o para armazenamento! =0A</body></html>
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