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[SPAM] [obm-l] RES: [obm-l] RES: [obm-l] Res: [obm-l] demonstração: pequeno teorema de FERMAT
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Pensei que o link tivesse ido...
=20
http://primes.utm.edu/notes/proofs/FermatsLittleTheorem.html
=20
Artur=20
-----Mensagem original-----
De: owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx]Em =
nome de ralonso
Enviada em: segunda-feira, 26 de novembro de 2007 16:25
Para: obm-l@xxxxxxxxxxxxxx
Assunto: Re: [obm-l] RES: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno =
teorema de FERMAT
qual link?=20
Artur Costa Steiner wrote:=20
Neste limk h=E1 uma provaArtur=20
-----Mensagem original-----=20
De: owner-obm-l@xxxxxxxxxxxxxx [ mailto:owner-obm-l@xxxxxxxxxxxxxx]Em =
nome de Rodrigo Cientista=20
Enviada em: segunda-feira, 26 de novembro de 2007 13:41=20
Para: obm-l@xxxxxxxxxxxxxx=20
Assunto: [obm-l] Res: [obm-l] demonstra=E7=E3o: pequeno teorema de =
FERMAT=20
=20
Salhab, realmente houve uma falha
=20
o teorema diz que n^p =3D=3Dn mod p, o que n=E3o sabemos...
=20
seja x um resto qualquer da divis=E3o de n por p, tal que n =3D=3D x mod =
p
=20
seja 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
=20
w =3D=3D r mod p implica w^p =3D=3D r^p mod p=20
=20
=20
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...)=20
=20
----- Mensagem original ----=20
De: Marcelo Salhab Brogliato <msbrogli@xxxxxxxxx>=20
Para: obm-l@xxxxxxxxxxxxxx=20
Enviadas: S=E1bado, 24 de Novembro de 2007 20:16:58=20
Assunto: Re: [obm-l] demonstra=E7=E3o: pequeno teorema de FERMAT=20
Ol=E1 Rodrigo,=20
n=E3o entendi essa passagem: x^p - x =3D=3D n^p - n =3D=3D 0 mod p ...=20
de onde veio o 0?=20
abra=E7os,=20
Salhab=20
=20
=20
On Nov 24, 2007 6:01 PM, Rodrigo Cientista < =
<mailto:rodrigocientista@xxxxxxxxxxxx> rodrigocientista@xxxxxxxxxxxx> =
wrote:=20
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:=20
o teorema diz que n^p =3D=3Dn mod p, o que n=E3o sabemos...=20
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)=20
n^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p (das propriedades =
de congru=EAncia)=20
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)=20
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=20
=20
Abra sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o =
para armazenamento!=20
http://br.mail.yahoo.com/=20
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=20
Instru=E7=F5es para entrar na lista, sair da lista e usar a lista em=20
http://www.mat.puc-rio.br/~obmlistas/obm-l.html =
<http://www.mat.puc-rio.br/%7Eobmlistas/obm-l.html> =20
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
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_____ =20
Abra sua conta no Yahoo! =
<http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.com/> =
Mail, o =FAnico sem limite de espa=E7o para armazenamento!
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<BODY>
<DIV><SPAN class=3D551430113-27112007><FONT face=3DArial color=3D#0000ff =
size=3D2>Pensei=20
que o link tivesse ido...</FONT></SPAN></DIV>
<DIV><SPAN class=3D551430113-27112007></SPAN> </DIV>
<DIV><SPAN class=3D551430113-27112007><FONT face=3DArial color=3D#0000ff =
size=3D2><A=20
href=3D"http://primes.utm.edu/notes/proofs/FermatsLittleTheorem.html";>htt=
p://primes.utm.edu/notes/proofs/FermatsLittleTheorem.html</A></FONT></SPA=
N></DIV>
<DIV><SPAN class=3D551430113-27112007></SPAN> </DIV>
<DIV><SPAN class=3D551430113-27112007><FONT face=3DArial color=3D#0000ff =
size=3D2>Artur</FONT> </SPAN></DIV>
<BLOCKQUOTE dir=3Dltr style=3D"MARGIN-RIGHT: 0px">
<DIV class=3DOutlookMessageHeader dir=3Dltr align=3Dleft><FONT =
face=3DTahoma=20
size=3D2>-----Mensagem original-----<BR><B>De:</B> =
owner-obm-l@xxxxxxxxxxxxxx=20
[mailto:owner-obm-l@xxxxxxxxxxxxxx]<B>Em nome de =
</B>ralonso<BR><B>Enviada=20
em:</B> segunda-feira, 26 de novembro de 2007 16:25<BR><B>Para:</B>=20
obm-l@xxxxxxxxxxxxxx<BR><B>Assunto:</B> Re: [obm-l] RES: [obm-l] Res: =
[obm-l]=20
demonstra=E7=E3o: pequeno teorema de FERMAT<BR><BR></FONT></DIV>qual =
link?=20
<P>Artur Costa Steiner wrote:=20
<BLOCKQUOTE TYPE=3D"CITE">
<STYLE type=3Dtext/css>DIV {
MARGIN: 0px
}
</STYLE>
<SPAN class=3D919372017-26112007><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D-1>Neste limk h=E1 uma prova</FONT></FONT></FONT></SPAN><SPAN =
class=3D919372017-26112007><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D-1>Artur</FONT></FONT></FONT></SPAN>=20
<BLOCKQUOTE>
<DIV class=3DOutlookMessageHeader dir=3Dltr><FONT =
face=3DTahoma><FONT=20
size=3D-1>-----Mensagem original-----</FONT></FONT> <BR><FONT=20
face=3DTahoma><FONT size=3D-1><B>De:</B> =
owner-obm-l@xxxxxxxxxxxxxx [<A=20
=
href=3D"mailto:owner-obm-l@xxxxxxxxxxxxxx";>mailto:owner-obm-l@xxxxxxxxxxx=
.br</A>]<B>Em=20
nome de </B>Rodrigo Cientista</FONT></FONT> <BR><FONT =
face=3DTahoma><FONT=20
size=3D-1><B>Enviada em:</B> segunda-feira, 26 de novembro de 2007 =
13:41</FONT></FONT> <BR><FONT face=3DTahoma><FONT =
size=3D-1><B>Para:</B>=20
obm-l@xxxxxxxxxxxxxx</FONT></FONT> <BR><FONT face=3DTahoma><FONT=20
size=3D-1><B>Assunto:</B> [obm-l] Res: [obm-l] demonstra=E7=E3o: =
pequeno teorema=20
de FERMAT</FONT></FONT> <BR> </DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">Salhab,=20
realmente houve uma falha</DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif"> </DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">o=20
teorema diz que n^p =3D=3Dn mod p, o que n=E3o sabemos...</DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif"> </DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">seja=20
x um resto qualquer da divis=E3o de n por p, tal que n =3D=3D x =
mod p</DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif"> </DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">seja=20
um k qualquer tal que x-k =3D 1 (chamarei de r) e n-k =3D w, assim =
n =3D=3D x mop=20
p =E9 equivalente a n - k =3D=3D x - k mop p que pode ser =
reescrito como w =3D=3D r=20
mod p</DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif"> </DIV>w=20
=3D=3D r mod p implica w^p =3D=3D r^p mod p <BR> <BR> =20
<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=20
demonstra o teorema quando w deixa resto 1 na divis=E3o por p, =
tentei provar=20
por indu=E7=E3o para w+1, mas n=E3o saiu...)=20
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">=20
<BR> </DIV>
<DIV=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, =
times, serif">-----=20
Mensagem original ---- <BR>De: Marcelo Salhab Brogliato=20
<msbrogli@xxxxxxxxx> <BR>Para: obm-l@xxxxxxxxxxxxxx =
<BR>Enviadas:=20
S=E1bado, 24 de Novembro de 2007 20:16:58 <BR>Assunto: Re: [obm-l] =
demonstra=E7=E3o: pequeno teorema de FERMAT=20
<P>Ol=E1 Rodrigo,=20
<P>n=E3o entendi essa passagem: x^p - x =3D=3D n^p - n =3D=3D 0 =
mod p ... <BR>de=20
onde veio o 0?=20
<P>abra=E7os, <BR>Salhab <BR> <BR> =20
<DIV class=3Dgmail_quote>On Nov 24, 2007 6:01 PM, Rodrigo =
Cientista <<A=20
href=3D"mailto:rodrigocientista@xxxxxxxxxxxx"; target=3D_blank =
rel=3Dnofollow=20
ymailto=3D"mailto:rodrigocientista@xxxxxxxxxxxx";>=20
rodrigocientista@xxxxxxxxxxxx</A>> wrote:=20
<BLOCKQUOTE class=3Dgmail_quote=20
style=3D"PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; =
BORDER-LEFT: rgb(204,204,204) 1px solid">Em=20
primeiro lugar ol=E1 a todos, sou novo na lista, e gostaria de =
saber se=20
uma demonstra=E7=E3o que dei para o pequeno teorema de fermat =
est=E1=20
equivocada ou n=E3o, conforme segue:=20
<P>o teorema diz que n^p =3D=3Dn mod p, o que n=E3o sabemos...=20
<P>escreverei n =3D=3D x mod p, assim n =3D=3D x mod p implica =
n^p =3D=3D x^p mod p=20
(das propriedades de congru=EAncia)=20
<P>n^p =3D=3D x^p mod p equivale a x^p =3D=3D n^p mod p (das =
propriedades de=20
congru=EAncia)=20
<P>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=20
propriedades de congru=EAncia)=20
<P>assim x^p - x =3D=3D n^p - n =3D=3D 0 mod p implica n^p =
=3D=3D n mod p como=20
quer=EDamos demonstrar <BR> =20
<P> Abra sua conta no Yahoo! Mail, o =
=FAnico sem=20
limite de espa=E7o para armazenamento! <BR><A=20
href=3D"http://br.mail.yahoo.com/"; target=3D_blank=20
rel=3Dnofollow>http://br.mail.yahoo.com/</A>=20
=
<P>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=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 entrar na lista, sair da lista e usar a =
lista em=20
<BR><A =
href=3D"http://www.mat.puc-rio.br/%7Eobmlistas/obm-l.html"=20
target=3D_blank=20
=
rel=3Dnofollow>http://www.mat.puc-rio.br/~obmlistas/obm-l.html</A>=20
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<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=
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