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Iran Contests
Iran MO (3rd Round)
1996 Iran MO (3rd Round)
4
Function
Function
Source: 14-th Iranian Mathematical Olympiad 1996/1997
October 17, 2005
function
algebra proposed
algebra
Problem Statement
Determine all functions
f
:
N
0
→
N
0
−
{
1
}
f : \mathbb N_0 \rightarrow \mathbb N_0 - \{1\}
f
:
N
0
→
N
0
−
{
1
}
such that
f
(
n
+
1
)
+
f
(
n
+
3
)
=
f
(
n
+
5
)
f
(
n
+
7
)
−
1375
,
∀
n
∈
N
.
f(n + 1) + f(n + 3) = f(n + 5)f(n + 7) - 1375, \qquad \forall n \in \mathbb N.
f
(
n
+
1
)
+
f
(
n
+
3
)
=
f
(
n
+
5
)
f
(
n
+
7
)
−
1375
,
∀
n
∈
N
.
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