MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2003 India IMO Training Camp
7
7
Part of
2003 India IMO Training Camp
Problems
(1)
Easy
Source: Iranian selection test for IMO 2004
6/27/2004
p
p
p
is a polynomial with integer coefficients and for every natural
n
n
n
we have
p
(
n
)
>
n
p(n)>n
p
(
n
)
>
n
.
x
k
x_k
x
k
is a sequence that:
x
1
=
1
,
x
i
+
1
=
p
(
x
i
)
x_1=1, x_{i+1}=p(x_i)
x
1
=
1
,
x
i
+
1
=
p
(
x
i
)
for every
N
N
N
one of
x
i
x_i
x
i
is divisible by
N
.
N.
N
.
Prove that
p
(
x
)
=
x
+
1
p(x)=x+1
p
(
x
)
=
x
+
1
algebra
polynomial
limit
number theory proposed
number theory