[SPAM] [obm-l] 2 PROBLEMAS - AJUDEM!

[MauZ <mauz.matematica@xxxxxxxxx>]

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   1. Seja P(x) um polin=F4mio com coeficientes inteiros tal que P(0) =3D
   P(1) =3D 1. Considere x0 um inteiro qualquer e defina xn+1 =3D P(xn) par=
a
   todo n =3D 0, 1, 2, 3,...... Prove que, para i diferente de j, xi e xj s=
=E3o
   primos entre si.
   2. Seja f : N* =E0 N* com f(n+1) > f(f(n)) para todo n pertencente aos
   N*. Prove que f(n)=3Dn.

Desde j=E1 agrade=E7o qualquer ajuda!!

Obrigado,
Maurizio

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<ol style=3D"margin-top: 0cm;" start=3D"1" type=3D"1"><li style=3D"color: n=
avy;"><font color=3D"navy" face=3D"Arial" size=3D"2"><span style=3D"font-si=
ze: 10pt; font-family: Arial;">Seja
     P(x) um polin=F4mio com coeficientes inteiros tal que P(0) =3D P(1) =
=3D 1. Considere
     x</span></font><sub><font face=3D"Arial (W1)"><span>0</span></font></s=
ub><font face=3D"Arial" size=3D"2"><span style=3D"font-size: 10pt; font-fam=
ily: Arial;"> um
     inteiro qualquer e defina x</span></font><sub><font face=3D"Arial (W1)=
"><span>n+1 </span></font></sub><font face=3D"Arial" size=3D"2"><span style=
=3D"font-size: 10pt; font-family: Arial;">=3D P(x</span></font><sub><font f=
ace=3D"Arial (W1)"><span>n</span></font></sub><font face=3D"Arial" size=3D"=
2"><span style=3D"font-size: 10pt; font-family: Arial;">) para
     todo n =3D 0, 1, 2, 3,...... Prove que, para i diferente de j, x</span=
></font><sub><font face=3D"Arial"><span style=3D"font-family: Arial;">i</sp=
an></font></sub><font face=3D"Arial"><span style=3D"font-family: Arial;"> <=
/span></font><font face=3D"Arial" size=3D"2"><span style=3D"font-size: 10pt=
; font-family: Arial;">e x</span></font><sub><font face=3D"Arial"><span sty=
le=3D"font-family: Arial;">j </span></font></sub><font face=3D"Arial" size=
=3D"2"><span style=3D"font-size: 10pt; font-family: Arial;">s=E3o
     primos entre si.</span></font></li><li style=3D"color: navy;"><font co=
lor=3D"navy" face=3D"Arial" size=3D"2"><span style=3D"font-size: 10pt; font=
-family: Arial;">Seja
     f : N* </span></font><font face=3D"Wingdings" size=3D"2"><span style=
=3D"font-size: 10pt; font-family: Wingdings;">=E0</span></font><font face=
=3D"Arial" size=3D"2"><span style=3D"font-size: 10pt; font-family: Arial;">=
 N* com f(n+1) &gt; f(f(n))
     para todo n pertencente aos N*. Prove que f(n)=3Dn.</span></font></li>=
</ol>Desde j=E1 agrade=E7o qualquer ajuda!!<br><br>Obrigado,<br>Maurizio<br=
>

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