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[SPAM] Re: [obm-l] Desigualdade envolvendo a sequencia dos primos
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Ol=E1 colega, boa tarde!
Eu tamb=E9m encontrei uma solu=E7=E3o bastante trivial,... "mas a margem =
=E9 muito pequena para cont=EA-la" ..... rssss
(brincadeirinha...)
Devemos manter o bom humor nesta lista, n=E3o =E9 mesmo?
Amplexo.
Fernando
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----- Original Message -----=20
From: Artur Costa Steiner=20
To: obm-l@xxxxxxxxxxxxxx=20
Sent: Monday, April 07, 2008 10:50 AM
Subject: [obm-l] Desigualdade envolvendo a sequencia dos primos
Acho este problema interessante. Encontrei uma solucao, gostaria de =
ver como os colegas resolvem.=20
Seja p_n, n =3D1,2,3.... a sequencia dos numeros primos. Mostre que, =
para todo k > 1, a desigualdade,=20
p_n < n^k
ocorre para uma infinidade de =EDndices n.
------=_NextPart_000_0016_01C898BB.1B1A8BD0
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charset="iso-8859-1"
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD><TITLE></TITLE>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2900.2912" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY text=3D#000000 bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Ol=E1 colega, boa tarde!</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Eu tamb=E9m encontrei uma solu=E7=E3o =
bastante=20
trivial,... "mas a margem =E9 muito pequena para cont=EA-la" .....=20
rssss</FONT></DIV>
<DIV><FONT face=3DArial=20
size=3D2> &nbs=
p;  =
; =20
(brincadeirinha...)</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Devemos manter o bom humor nesta lista, =
n=E3o =E9=20
mesmo?</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=3DArial size=3D2>Amplexo.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Fernando</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV>
<HR>
<HR>
</DIV>
<BLOCKQUOTE dir=3Dltr=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=3Dartur.steiner@xxxxxxxxxx =
href=3D"mailto:artur.steiner@xxxxxxxxxx";>Artur=20
Costa Steiner</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> Monday, April 07, 2008 =
10:50=20
AM</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [obm-l] Desigualdade =
envolvendo=20
a sequencia dos primos</DIV>
<DIV><BR></DIV>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2> Acho este <SPAN =
class=3D352134513-07042008>problema=20
interessante. Encontrei uma solucao, gostaria de ver como os =
colegas=20
resolvem. </SPAN></FONT></FONT></FONT></SPAN></DIV>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN=20
=
class=3D352134513-07042008></SPAN></FONT></FONT></FONT></SPAN> </DIV=
>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN class=3D352134513-07042008>Seja p_n, n =3D1,2,3.... a =
sequencia dos=20
numeros primos. Mostre que, para todo k > 1, a desigualdade,=20
</SPAN></FONT></FONT></FONT></SPAN></DIV>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN=20
=
class=3D352134513-07042008></SPAN></FONT></FONT></FONT></SPAN> </DIV=
>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN class=3D352134513-07042008>p_n <=20
n^k</SPAN></FONT></FONT></FONT></SPAN></DIV>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN=20
=
class=3D352134513-07042008></SPAN></FONT></FONT></FONT></SPAN> </DIV=
>
<DIV><SPAN class=3D352134513-07042008><FONT face=3DArial><FONT =
color=3D#0000ff><FONT=20
size=3D2><SPAN class=3D352134513-07042008>ocorre para uma infinidade =
de =EDndices=20
n.</SPAN></FONT></FONT></FONT></SPAN></DIV></BLOCKQUOTE></BODY></HTML>
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