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

[Rodrigo Cientista <rodrigocientista@xxxxxxxxxxxx>]

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Salhab, realmente houve uma falha=0A=0Ao teorema diz que n^p =3D=3Dn mod p,=
 o que n=E3o sabemos...=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 (cha=
marei 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=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 quand=
o 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----- Mensagem original ----=0ADe: Marcelo=
 Salhab Brogliato <msbrogli@xxxxxxxxx>=0APara: obm-l@xxxxxxxxxxxxxx=0AEnvia=
das: S=E1bado, 24 de Novembro de 2007 20:16:58=0AAssunto: Re: [obm-l] demon=
stra=E7=E3o: pequeno teorema de FERMAT=0A=0AOl=E1 Rodrigo,=0A=0An=E3o enten=
di 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=0AOn Nov 24, 2007 6:01 PM, Rodrigo C=
ientista < 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, confo=
rme 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 propriedades de congru=EAncia) =0A=0A=
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 mo=
d 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 par=
a 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/~obm=
listas/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      Abra sua conta no Yahoo! Mail, o =FAnico sem =
limite 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">Salhab, realmente houve uma falha</DIV>=0A<DIV st=
yle=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, seri=
f">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new rom=
an, new york, times, serif">o teorema diz que n^p =3D=3Dn mod p, o que n=E3=
o 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&nbsp;x um rest=
o qualquer da divis=E3o de n por p, tal que n =3D=3D x mod p</DIV>=0A<DIV s=
tyle=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, ser=
if">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new ro=
man, new york, times, serif">seja&nbsp;um k qualquer tal que x-k =3D 1 (cha=
marei 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 =
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, se=
rif">&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 yo=
rk, times, serif"><BR><BR>&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FON=
T-FAMILY: times new roman, new york, times, serif">----- Mensagem original =
----<BR>De: Marcelo Salhab Brogliato &lt;msbrogli@xxxxxxxxx&gt;<BR>Para: ob=
m-l@xxxxxxxxxxxxxx<BR>Enviadas: S=E1bado, 24 de Novembro de 2007 20:16:58<B=
R>Assunto: Re: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT<BR><BR>O=
l=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=3D=
nofollow ymailto=3D"mailto:rodrigocientista@xxxxxxxxxxxx";> rodrigocientista=
@yahoo.com.br</A>&gt; wrote:<BR>=0A<BLOCKQUOTE class=3Dgmail_quote style=3D=
"PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: rgb(204,204,204=
) 1px solid">Em 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: <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, a=
ssim n =3D=3D x mod p implica n^p =3D=3D x^p mod p (das propriedades de con=
gru=EAncia)<BR><BR>n^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p (da=
s 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 congru=EA=
ncia)<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;Abra su=
a 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=0A=0A      <hr size=3D1>Abra sua conta=
 no <a href=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.ya=
hoo.com/">Yahoo! Mail</a>, o =FAnico sem limite de espa=E7o para armazename=
nto! =0A</body></html>
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