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Poland - Second Round
2016 Poland - Second Round
3
3
Part of
2016 Poland - Second Round
Problems
(1)
Function on integers
Source: 67 Polish MO 2016 Second Round - Problem 3
4/30/2018
Determine, whether exists function
f
f
f
, which assigns each integer
k
k
k
, nonnegative integer
f
(
k
)
f(k)
f
(
k
)
and meets the conditions:
f
(
0
)
>
0
f(0) > 0
f
(
0
)
>
0
, for each integer
k
k
k
minimal number of the form
f
(
k
−
l
)
+
f
(
l
)
f(k - l) + f(l)
f
(
k
−
l
)
+
f
(
l
)
, where
l
∈
Z
l \in \mathbb{Z}
l
∈
Z
, equals
f
(
k
)
f(k)
f
(
k
)
.
algebra
function
Poland