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International Contests
Nordic
1999 Nordic
1
1
Part of
1999 Nordic
Problems
(1)
f(n) = f(f(n + 11)) if n<=1999, f(n) = n - 5 if n > 1999
Source: Nordic Mathematical Contest 1999 #1
10/3/2017
The function
f
f
f
is defined for non-negative integers and satisfies the condition
f
(
n
)
=
f
(
f
(
n
+
11
)
)
f(n) = f(f(n + 11))
f
(
n
)
=
f
(
f
(
n
+
11
))
, if
n
≤
1999
n \le 1999
n
≤
1999
and
f
(
n
)
=
n
−
5
f(n) = n - 5
f
(
n
)
=
n
−
5
, if
n
>
1999
n > 1999
n
>
1999
. Find all solutions of the equation
f
(
n
)
=
1999
f(n) = 1999
f
(
n
)
=
1999
.
functional equation
algebra