[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[SPAM] [obm-l] Re: [obm-l] Re: [obm-l] OBM TERCEIRA FASE – NÍVEL 3 -- 2ª questão



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:   (9.00 hits, 5 required)
SPAM: REFERENCES         (-0.5 points) Has a valid-looking References header
SPAM: X_MAILING_LIST     (-0.3 points) Found a X-Mailing-List header
SPAM: NO_REAL_NAME       (1.3 points)  From: does not include a real name
SPAM: USER_AGENT_OE      (0.2 points)  X-Mailer header indicates a non-spam MUA (Outlook Express)
SPAM: SPAM_PHRASE_00_01  (0.8 points)  BODY: Spam phrases score is 00 to 01 (low)
SPAM:                    [score: 0]
SPAM: BIG_FONT           (0.3 points)  BODY: FONT Size +2 and up or 3 and up
SPAM: HTML_FONT_FACE_ODD (0.3 points)  BODY: HTML font face is not a commonly used face
SPAM: MAILTO_LINK        (0.2 points)  BODY: Includes a URL link to send an email
SPAM: SUPERLONG_LINE     (0.0 points)  BODY: Contains a line >=199 characters long
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 165.84.191.209.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 165.84.191.209.relays.osirusoft.com.]
SPAM: X_OSIRU_OPEN_RELAY (2.7 points)  RBL: DNSBL: sender is Confirmed Open Relay
SPAM: AWL                (-1.4 points) AWL: Auto-whitelist adjustment
SPAM: 
SPAM: -------------------- End of SpamAssassin results ---------------------

This is a multi-part message in MIME format.

------=_NextPart_000_0029_01C8C0A9.6B577980
Content-Type: text/plain;
	charset="utf-8"
Content-Transfer-Encoding: quoted-printable

Douglas, desculpe-me, li mal o problema, a minha solu=C3=A7=C3=A3o segue =
abaixo:

como c + x^2 =C3=A9 m=C3=BAltiplo de 2^2007, ent=C3=A3o c + x^2 =3D =
w2^2007

partimos de duas constata=C3=A7=C3=B5es:

a) um quadrado perfeito par =C3=A9 divis=C3=ADvel por 4

**prova: tome x^2 par =3D=3D> x =C3=A9 par =3D=3D> x =3D 2k =3D=3D: x^2 =
=3D 4k^2

b) um quadrado perfeito =C3=ADmpar =C3=A9 da forma 8a + 1

**prova: tome x^2 =C3=ADmpar =3D=3D> x =C3=A9 =C3=ADmpar =3D=3D> x =
=C3=A9 da forma 2n+1 =3D=3D> x^2 =3D (2n+1)^2 =3D 4n^2 + 4n + 1 =3D =
4n(n+1) + 1, como n e n+1 s=C3=A3o consecutivos, um deles =C3=A9 par, =
logo n(n+1) por ser escrito como 2a =3D=3D> 4n(n+1) + 1 =3D 8a + 1 =3D =
x^2

1 ) no caso em que x^2 =C3=A9 par, temos que x^2 =3D 4k^2 =3D=3D> c =3D =
w2^2007 - 4k^2, como 4 divide 2^2007 =3D=3D> 4 divide w2^2007 - 4k^2 =
=3D=3D> 4 divide c, logo c assume os valores m=C3=BAltiplos de 4 no =
intervalo [-2007, 2007] (para que sua soma com um x^2 suficientemente =
grande seja divis=C3=ADvel por 2^2007), incluindo o zero, que s=C3=A3o =
no total de 501 + 501 + 1 =3D 1003 (4 divide 2007 - 3 em 501 partes, =
mesmo racioc=C3=ADnio para 3 - 2007)

2 ) no caso em que x^2 =C3=A9 =C3=ADmpar, temos que x^2 =3D 8a + 1 =
=3D=3D> c + 8a + 1 =3D w2^2007 =3D=3D> c + 1 =3D w2^2007 - 8a, como 8 =
divide w2^2007 - 8a =3D=3D> 8 divide c + 1, logo c assume os valores que =
somados a 1 s=C3=A3o m=C3=BAltiplos de 8 no intervalo [-2007, 2007] =
(para que sua soma com um x^2 suficientemente grande seja divis=C3=ADvel =
por 2^2007, mesmo racioc=C3=ADnio), excluindo o zero pois j=C3=A1 foi =
contado, que s=C3=A3o no total de 250 + 250 =3D 500 (8 divide 2007 - 7 =
em 250 partes, mesmo racioc=C3=ADnio para 7 - 2007)

RESP: para 1503 inteiros c
  ----- Original Message -----=20
  From: douglas paula=20
  To: obm-l@xxxxxxxxxxxxxx=20
  Sent: Tuesday, May 27, 2008 9:44 PM
  Subject: Re: [obm-l] Re: [obm-l] OBM TERCEIRA FASE =
=C3=A2=E2=82=AC=E2=80=9C N=C3=83=C2=8DVEL 3 -- 2=C3=82=C2=AA =
quest=C3=83=C2=A3o


  rodrigo,

   ao meu ver, c + x^2 =3D k 2^2007 , onde k =C3=A9 qq natural e k =
2^2007 n=C3=A3o =C3=A9 necessariamente igual =C3=A0 2^n

  venho a um bom tempo quebrando a cabe=C3=A7a nessa quest=C3=A3o mas =
sem conseguir muito resultado ...

  rodrigocientista@xxxxxxxxxxxx escreveu:
    =C3=AF=C2=BB=C2=BF=20
    vou tentar,

    2^n - x^2 =3D c tal qque 1< n < 2007, como todo n=C3=83=C2=BAmero =
pode ser expresso como diferen=C3=83=C2=A7a de dois quadrados, =
s=C3=83=C2=B3 existem "c" tal que n possa ser um quadrado, de sorte que =
c seja expresso como diferen=C3=83=C2=A7a de dois quadrados


      ----- Original Message -----=20
      From: douglas paula=20
      To: obm-l@xxxxxxxxxxxxxx=20
      Sent: Saturday, May 17, 2008 11:02 PM
      Subject: [obm-l] OBM TERCEIRA FASE =C3=A2=E2=82=AC=E2=80=9C =
N=C3=83=C2=8DVEL 3 -- 2=C3=82=C2=AA quest=C3=83=C2=A3o


      XXIX OLIMP=C3=83=C2=8DADA BRASILEIRA DE MATEM=C3=83=C2=81TICA
      TERCEIRA FASE =C3=A2=E2=82=AC=E2=80=9C N=C3=83=C2=8DVEL 3 (Ensino =
M=C3=83=C2=A9dio)
      PRIMEIRO DIA

      PROBLEMA 2
      Para quantos n=C3=BAmeros inteiros c, - 2007 <=3D c <=3D 2007 , =
existe um inteiro x tal que x^2 + c =C3=A9 m=C3=BAltiplo de 2^2007?=20

      algu=C3=A9m se habilita?

      grato,=20
                       Douglas

-------------------------------------------------------------------------=
-
      Abra sua conta no Yahoo! Mail, o =C3=83=C2=BAnico sem limite de =
espa=C3=83=C2=A7o para armazenamento!=20




-------------------------------------------------------------------------=
-----
  Abra sua conta no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o =
para armazenamento! 
------=_NextPart_000_0029_01C8C0A9.6B577980
Content-Type: text/html;
	charset="utf-8"
Content-Transfer-Encoding: quoted-printable

=EF=BB=BF<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; charset=3Dutf-8">
<META content=3D"MSHTML 6.00.2900.3314" name=3DGENERATOR></HEAD>
<BODY bgColor=3D#ffffff>
<DIV>
<DIV><FONT face=3DArial size=3D2>Douglas, desculpe-me, li mal o =
problema, a minha=20
solu=C3=A7=C3=A3o segue abaixo:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>como c + x^2 =C3=A9 m=C3=BAltiplo de =
2^2007, ent=C3=A3o c + x^2 =3D=20
w2^2007</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>partimos de duas =
constata=C3=A7=C3=B5es:</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>a) um quadrado perfeito par =C3=A9 =
divis=C3=ADvel por=20
4</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>**prova: tome x^2 par =3D=3D&gt; x =
=C3=A9 par =3D=3D&gt; x =3D 2k=20
=3D=3D: x^2 =3D 4k^2</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>b) um quadrado perfeito =C3=ADmpar =
=C3=A9 da forma 8a +=20
1</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>**prova: tome x^2 =C3=ADmpar =3D=3D&gt; =
x =C3=A9 =C3=ADmpar =3D=3D&gt; x =C3=A9=20
da forma 2n+1 =3D=3D&gt; x^2 =3D (2n+1)^2 =3D 4n^2 + 4n + 1 =3D 4n(n+1) =
+ 1, como n e n+1=20
s=C3=A3o consecutivos, um deles =C3=A9 par, logo n(n+1)&nbsp;por ser =
escrito como 2a=20
=3D=3D&gt; 4n(n+1) + 1 =3D 8a + 1 =3D x^2</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>1 ) no caso em que x^2 =C3=A9 par, =
temos que x^2 =3D 4k^2=20
=3D=3D&gt; c =3D w2^2007 - 4k^2, como 4 divide 2^2007 =3D=3D&gt; 4 =
divide w2^2007 - 4k^2=20
=3D=3D&gt; 4 divide c, logo c assume os valores m=C3=BAltiplos de 4 no =
intervalo [-2007,=20
2007] (para que sua soma com um x^2 suficientemente grande seja =
divis=C3=ADvel por=20
2^2007), incluindo o zero, que s=C3=A3o no total de&nbsp;501 + 501 + 1 =
=3D 1003 (4=20
divide 2007 - 3 em 501 partes, mesmo racioc=C3=ADnio para 3 - =
2007)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>2 ) no caso em que x^2 =C3=A9 =
=C3=ADmpar, temos que x^2 =3D 8a=20
+ 1 =3D=3D&gt; c + 8a + 1 =3D w2^2007 =3D=3D&gt; c + 1 =3D w2^2007 - 8a, =
como 8 divide=20
w2^2007 - 8a =3D=3D&gt; 8 divide c + 1, logo c assume os valores que =
somados a 1 s=C3=A3o=20
m=C3=BAltiplos de 8 no intervalo [-2007, 2007] (para que sua soma com um =
x^2=20
suficientemente grande seja divis=C3=ADvel por 2^2007, mesmo =
racioc=C3=ADnio), excluindo o=20
zero pois j=C3=A1 foi contado, que s=C3=A3o no total de 250 + 250 =3D =
500 (8 divide 2007 - 7=20
em 250 partes, mesmo racioc=C3=ADnio para 7 - 2007)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>RESP: para 1503 inteiros =
c</FONT></DIV></DIV>
<BLOCKQUOTE=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=3Ddouglasfogo@xxxxxxxxxxxx=20
  href=3D"mailto:douglasfogo@xxxxxxxxxxxx";>douglas paula</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
  href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Tuesday, May 27, 2008 =
9:44 PM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> Re: [obm-l] Re: =
[obm-l] OBM=20
  TERCEIRA FASE =C3=A2=E2=82=AC=E2=80=9C N=C3=83=C2=8DVEL 3 -- =
2=C3=82=C2=AA quest=C3=83=C2=A3o</DIV>
  <DIV><BR></DIV>
  <DIV>rodrigo,</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>&nbsp;ao meu ver, c + x^2 =3D k 2^2007 , onde k =C3=A9 qq natural =
e k 2^2007 n=C3=A3o=20
  =C3=A9 necessariamente igual =C3=A0 2^n</DIV>
  <DIV>&nbsp;</DIV>
  <DIV>venho a um bom tempo quebrando a cabe=C3=A7a nessa quest=C3=A3o =
mas sem conseguir=20
  muito resultado ...</DIV>
  <DIV><BR><B><I><A=20
  =
href=3D"mailto:rodrigocientista@xxxxxxxxxxxx";>rodrigocientista@xxxxxxxxxx=
br</A></I></B>=20
  escreveu:</DIV>
  <BLOCKQUOTE class=3Dreplbq=20
  style=3D"PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px =
solid">=C3=AF=C2=BB=C2=BF=20

    <META content=3D"MSHTML 6.00.2900.3314" name=3DGENERATOR>
    <STYLE></STYLE>

    <DIV><FONT face=3DArial size=3D2>vou tentar,</FONT></DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial size=3D2>2^n - x^2 =3D c tal qque 1&lt; n =
&lt; 2007, como=20
    todo n=C3=83=C2=BAmero pode ser expresso como diferen=C3=83=C2=A7a =
de dois quadrados, s=C3=83=C2=B3=20
    existem "c" tal que n possa ser um quadrado, de sorte que c seja =
expresso=20
    como diferen=C3=83=C2=A7a de dois quadrados</FONT></DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
    <BLOCKQUOTE=20
    style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
      <DIV style=3D"FONT: 10pt arial">----- Original Message ----- =
</DIV>
      <DIV=20
      style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
      <A title=3Ddouglasfogo@xxxxxxxxxxxx=20
      href=3D"mailto:douglasfogo@xxxxxxxxxxxx";>douglas paula</A> </DIV>
      <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
      href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> =
</DIV>
      <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Saturday, May 17, =
2008 11:02=20
      PM</DIV>
      <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [obm-l] OBM =
TERCEIRA FASE=20
      =C3=A2=E2=82=AC=E2=80=9C N=C3=83=C2=8DVEL 3 -- 2=C3=82=C2=AA =
quest=C3=83=C2=A3o</DIV>
      <DIV><BR></DIV><B><FONT face=3DArialNarrow-Bold>
      <DIV align=3Dleft>XXIX OLIMP=C3=83=C2=8DADA BRASILEIRA DE =
MATEM=C3=83=C2=81TICA</DIV>
      <DIV align=3Dleft>TERCEIRA FASE =C3=A2=E2=82=AC=E2=80=9C =
N=C3=83=C2=8DVEL 3 (Ensino M=C3=83=C2=A9dio)</DIV>
      <DIV>PRIMEIRO DIA</DIV>
      <DIV>&nbsp;</DIV><B><FONT face=3DArialNarrow-Bold size=3D2>
      <DIV align=3Dleft>PROBLEMA 2</DIV></B></FONT><FONT =
face=3DTimesNewRoman=20
size=3D3>
      <DIV>Para quantos n=C3=BAmeros inteiros c,&nbsp;- =
2007&nbsp;&lt;=3D c&nbsp;&lt;=3D=20
      2007 , existe um inteiro x tal que x^2 + c =C3=A9 m=C3=BAltiplo de =
2^2007?=20
      </FONT></DIV>
      <DIV><FONT face=3DTimesNewRoman size=3D3></FONT>&nbsp;</DIV>
      <DIV><FONT face=3DTimesNewRoman size=3D3>algu=C3=A9m se =
habilita?</FONT></DIV>
      <DIV><FONT face=3DTimesNewRoman size=3D3></FONT>&nbsp;</DIV>
      <DIV><FONT face=3DTimesNewRoman size=3D3>grato, </FONT></DIV>
      <DIV><FONT face=3DTimesNewRoman=20
      =
size=3D3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=20
      Douglas</DIV></FONT></B></FONT>
      <DIV>
      <HR SIZE=3D1>
      Abra sua conta no <A=20
      =
href=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.c=
om/">Yahoo!=20
      Mail</A>, o =C3=83=C2=BAnico sem limite de espa=C3=83=C2=A7o para =
armazenamento!=20
    </DIV></BLOCKQUOTE></BLOCKQUOTE><BR>
  <P>
  <HR SIZE=3D1>
  Abra sua conta no <A=20
  =
href=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.c=
om/">Yahoo!=20
  Mail</A>, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento!=20
</BLOCKQUOTE></BODY></HTML>

------=_NextPart_000_0029_01C8C0A9.6B577980--

=========================================================================
Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================