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

[Rodrigo Cientista <rodrigocientista@xxxxxxxxxxxx>]

SPAM: -------------------- Start SpamAssassin results ----------------------
SPAM: This mail is probably spam.  The original message has been altered
SPAM: so you can recognise or block similar unwanted mail in future.
SPAM: See http://spamassassin.org/tag/ for more details.
SPAM: 
SPAM: Content analysis details:   (8.10 hits, 5 required)
SPAM: X_MAILING_LIST     (-0.3 points) Found a X-Mailing-List header
SPAM: MIME_BOUND_DIGITS_5 (1.7 points)  Spam tool pattern in MIME boundary
SPAM: EMAIL_ATTRIBUTION  (-1.6 points) BODY: Contains what looks like an email attribution
SPAM: SPAM_PHRASE_00_01  (0.8 points)  BODY: Spam phrases score is 00 to 01 (low)
SPAM:                    [score: 0]
SPAM: HTML_FONT_COLOR_BLUE (0.2 points)  BODY: HTML font color is blue
SPAM: MAILTO_LINK        (0.2 points)  BODY: Includes a URL link to send an email
SPAM: MIME_EXCESSIVE_QP  (1.0 points)  RAW: Excessive quoted-printable encoding in body
SPAM: SPAM_REDIRECTOR    (0.4 points)  URI: Uses open redirection service
SPAM: FORGED_YAHOO_RCVD  (1.4 points)  'From' yahoo.com does not match 'Received' headers
SPAM: RCVD_IN_ORBS       (2.2 points)  RBL: Received via a relay in orbs.dorkslayers.com
SPAM:                    [RBL check: found 249.38.190.206.orbs.dorkslayers.com., type: 68.178.232.99]
SPAM: RCVD_IN_OSIRUSOFT_COM (0.4 points)  RBL: Received via a relay in relays.osirusoft.com
SPAM:                    [RBL check: found 249.38.190.206.relays.osirusoft.com.]
SPAM: X_OSIRU_OPEN_RELAY (2.7 points)  RBL: DNSBL: sender is Confirmed Open Relay
SPAM: AWL                (-1.0 points) AWL: Auto-whitelist adjustment
SPAM: 
SPAM: -------------------- End of SpamAssassin results ---------------------

--0-519349306-1196176313=:17509
Content-Type: text/plain; charset=iso-8859-1
Content-Transfer-Encoding: quoted-printable

S=F3 uma pequena corre=E7=E3o, na =FAtima passagem eu coloquei (n+1)^p =3D=
=3D n + 1 mod p mas foi por acidente que o 1 ficou ali, esqueci de apag=E1-=
lo (vejo que na lista n=E3o h=E1 muitos entusiastas por provas)=0A=0Aabra=
=E7os=0A=0A=0A=0A----- Mensagem original ----=0ADe: Rodrigo Cientista <rodr=
igocientista@xxxxxxxxxxxx>=0APara: obm-l@xxxxxxxxxxxxxx=0AEnviadas: Segunda=
-feira, 26 de Novembro de 2007 21:54:53=0AAssunto: [obm-l] Res: [obm-l] RES=
: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT=0A=0A=0A=
=0A=0APor indu=E7=E3o, =E9 simples!!=0A =0ASabemos que n^p =3D=3D n mop p p=
ara algum n(n=3D1, por exemplo), queremos saber se =E9 v=E1lido para todo n=
.=0A =0Aexpandindo, (n+1)^p =3D n^p + C_p,1*a^p-1 + ... + C_p,k*a^p-k + ...=
 + 1=0A =0Aobs*** C_x,y =3D combina=E7=E3o de x e y=0A =0AComo p divide C_p=
,k (pois o numerador =E9 p! =3D p(p-1)(p-2)...), segue (n+1)^p =3D=3D n^p +=
 1 mod p=0A =0AMas por hip=F3tese de indu=E7=E3o, j=E1 estava provado que n=
^p =3D=3D n mop p oq implica n^p +1 =3D=3D n + 1 mop p=0A =0AAssim, (n+1)^p=
 =3D=3D n + 1 mod p, provando Fermat por indu=E7=E3o sobre n=0A =0ARealment=
e, essa =E9 a prova mais simples, mas n=E3o =E9 minha=0A =0A-----Mensagem o=
riginal-----=0ADe: owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxx=
io.br]Em nome de Rodrigo Cientista=0AEnviada em: segunda-feira, 26 de novem=
bro de 2007 13:41=0APara: obm-l@xxxxxxxxxxxxxx=0AAssunto: [obm-l] Res: [obm=
-l] demonstra=E7=E3o: pequeno teorema de FERMAT=0A=0A=0ASalhab, realmente h=
ouve uma falha=0A =0Ao teorema diz que n^p =3D=3Dn mod p, o que n=E3o sabem=
os...=0A =0Aseja x um resto qualquer da divis=E3o de n por p, tal que n =3D=
=3D x mod p=0A =0Aseja 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 =0A =0Aw =3D=3D r mod p implic=
a w^p =3D=3D r^p mod p =0A =0Aw^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 rest=
o 1 na divis=E3o por p, tentei provar por indu=E7=E3o para w+1, mas n=E3o s=
aiu...)=0A=0A=0A =0A----- Mensagem original ----=0ADe: Marcelo Salhab Brogl=
iato <msbrogli@xxxxxxxxx>=0APara: 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 passa=
gem: x^p - x =3D=3D n^p - n =3D=3D 0 mod p ...=0Ade onde veio o 0?=0A=0Aabr=
a=E7os,=0ASalhab=0A=0A=0A=0AOn Nov 24, 2007 6:01 PM, Rodrigo Cientista < ro=
drigocientista@xxxxxxxxxxxx> wrote:=0A=0AEm primeiro lugar ol=E1 a todos, s=
ou 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=0Aescreve=
rei 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 propriedades de congru=EAncia) =0A=0Ase n =3D=3D x m=
od p e x^p =3D=3D n^p mod p ent=E3o n + x^p =3D=3D x+ n^p mod p (das propri=
edades de congru=EAncia)=0A=0Aassim x^p - x =3D=3D n^p - n =3D=3D 0 mod p i=
mplica 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.ht=
ml=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 lim=
ite de espa=E7o para armazenamento! =0A=0A=0A=0A=0A=0AAbra sua conta no Yah=
oo! Mail, o =FAnico sem limite de espa=E7o para armazenamento!=0A=0A=0A    =
  Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para arma=
zenamento!=0Ahttp://br.mail.yahoo.com/
--0-519349306-1196176313=:17509
Content-Type: text/html; charset=iso-8859-1
Content-Transfer-Encoding: quoted-printable

<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">S=F3 uma pequena corre=E7=E3o, na =FAtima passage=
m eu coloquei <FONT face=3DArial color=3D#0000ff size=3D2>(n+1)^p =3D=3D n =
+ 1 mod p mas foi por acidente que o 1 ficou ali, esqueci de apag=E1-lo (ve=
jo que na lista n=E3o h=E1 muitos entusiastas por provas)</FONT></DIV>=0A<P=
><FONT face=3DArial color=3D#0000ff size=3D2></FONT>&nbsp;</P>=0A<P><FONT f=
ace=3DArial color=3D#0000ff size=3D2>abra=E7os</FONT></P>=0A<DIV style=3D"F=
ONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif"><BR><=
BR></DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, ne=
w york, times, serif">----- Mensagem original ----<BR>De: Rodrigo Cientista=
 &lt;rodrigocientista@xxxxxxxxxxxx&gt;<BR>Para: obm-l@xxxxxxxxxxxxxx<BR>Env=
iadas: Segunda-feira, 26 de Novembro de 2007 21:54:53<BR>Assunto: [obm-l] R=
es: [obm-l] RES: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teorema de =
FERMAT<BR><BR>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roma=
n, new york, times, serif">=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: t=
imes new roman, new york, times, serif"><BR>=0A<DIV style=3D"FONT-SIZE: 12p=
t; FONT-FAMILY: times new roman, new york, times, serif">=0A<DIV><FONT face=
=3DArial color=3D#0000ff size=3D2>Por indu=E7=E3o, =E9 simples!!</FONT></DI=
V>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2></FONT>&nbsp;</DIV>=
=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2>Sabemos que n^p =3D=3D =
n mop p para algum n(n=3D1, por exemplo), queremos saber se =E9 v=E1lido pa=
ra todo n.</FONT></DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2>=
</FONT>&nbsp;</DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2>expa=
ndindo, (n+1)^p =3D n^p + C_p,1*a^p-1 + ... + C_p,k*a^p-k + ... + 1</FONT><=
/DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2></FONT>&nbsp;</DIV=
>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2>obs*** C_x,y =3D combi=
na=E7=E3o de x e y</FONT></DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff s=
ize=3D2></FONT>&nbsp;</DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff size=
=3D2>Como p divide C_p,k (pois o numerador =E9 p! =3D p(p-1)(p-2)...), segu=
e (n+1)^p =3D=3D n^p + 1 mod p</FONT></DIV>=0A<DIV><FONT face=3DArial color=
=3D#0000ff size=3D2></FONT>&nbsp;</DIV>=0A<DIV><FONT face=3DArial color=3D#=
0000ff size=3D2>Mas por hip=F3tese de indu=E7=E3o, j=E1 estava provado que =
n^p =3D=3D n mop p oq implica n^p +1 =3D=3D n + 1 mop p</FONT></DIV>=0A<DIV=
><FONT face=3DArial color=3D#0000ff size=3D2></FONT>&nbsp;</DIV>=0A<DIV><FO=
NT face=3DArial color=3D#0000ff size=3D2>Assim, (n+1)^p =3D=3D n + 1 mod p,=
 provando Fermat por indu=E7=E3o sobre n</FONT></DIV>=0A<DIV><FONT face=3DA=
rial color=3D#0000ff size=3D2></FONT>&nbsp;</DIV>=0A<DIV><FONT face=3DArial=
 color=3D#0000ff size=3D2>Realmente, essa =E9 a prova mais simples, mas n=
=E3o =E9 minha</FONT></DIV>=0A<DIV>&nbsp;</DIV>=0A<DIV><FONT face=3DTahoma =
size=3D2>-----Mensagem original-----<BR><B>De:</B> owner-obm-l@xxxxxxxxxxxx=
br [mailto:owner-obm-l@xxxxxxxxxxxxxx]<B>Em nome de </B>Rodrigo Cientista<B=
R><B>Enviada em:</B> segunda-feira, 26 de novembro de 2007 13:41<BR><B>Para=
:</B> obm-l@xxxxxxxxxxxxxx<BR><B>Assunto:</B> [obm-l] Res: [obm-l] demonstr=
a=E7=E3o: pequeno teorema de FERMAT<BR><BR></DIV></FONT>=0A<BLOCKQUOTE>=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: times new roman, ne=
w 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: times new roman,=
 new york, times, serif">o teorema diz que n^p =3D=3Dn mod p, o que n=E3o s=
abemos...</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new rom=
an, new york, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; F=
ONT-FAMILY: times new roman, new york, times, serif">seja&nbsp;x um resto q=
ualquer da divis=E3o de n por p, tal que n =3D=3D x mod p</DIV>=0A<DIV styl=
e=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&nbsp;um k qualquer tal que x-k =3D 1 (chamar=
ei 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 </DIV>=0A<DIV sty=
le=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 mod 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 resto 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, t=
imes, serif"><BR><BR>&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAM=
ILY: times new roman, new york, times, serif">----- Mensagem original ----<=
BR>De: Marcelo Salhab Brogliato &lt;msbrogli@xxxxxxxxx&gt;<BR>Para: obm-l@m=
at.puc-rio.br<BR>Enviadas: S=E1bado, 24 de Novembro de 2007 20:16:58<BR>Ass=
unto: Re: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT<BR><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 Cientista &lt;<A =
href=3D"mailto:rodrigocientista@xxxxxxxxxxxx"; target=3D_blank rel=3Dnofollo=
w ymailto=3D"mailto:rodrigocientista@xxxxxxxxxxxx";> rodrigocientista@yahoo.=
com.br</A>&gt; wrote:<BR>=0A<BLOCKQUOTE class=3Dgmail_quote style=3D"PADDIN=
G-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: rgb(204,204,204) 1px s=
olid">Em primeiro lugar ol=E1 a todos, sou novo na lista, e gostaria de sab=
er se uma demonstra=E7=E3o que dei para o pequeno teorema de fermat 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=EAn=
cia)<BR><BR>n^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p (das propr=
iedades 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 congru=EAncia)<B=
R><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;Abra sua conta=
 no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazenamento! <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=
=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></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><BR></DIV></DIV><BR>=0A<HR SI=
ZE=3D1>=0AAbra sua conta no <A href=3D"http://br.rd.yahoo.com/mail/taglines=
/mail/*http://br.mail.yahoo.com/"; target=3D_blank rel=3Dnofollow>Yahoo! Mai=
l</A>, o =FAnico sem limite de espa=E7o para armazenamento! </DIV>=0A<DIV s=
tyle=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, ser=
if"><BR></DIV></div><br>=0A=0A=0A      <hr size=3D1>Abra sua conta no <a hr=
ef=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.com/"=
>Yahoo! Mail</a>, o =FAnico sem limite de espa=E7o para armazenamento! =0A<=
/body></html>
--0-519349306-1196176313=:17509--
=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================