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KoMaL A Problems
KoMaL A Problems 2023/2024
A. 880
A. 880
Part of
KoMaL A Problems 2023/2024
Problems
(1)
Function with weighted sum always negative
Source: Komal A880
5/15/2024
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of real numbers for which there exists a function
f
:
Z
+
→
Z
+
f:\mathbb{Z}^{+}\rightarrow\mathbb{Z}^{+}
f
:
Z
+
→
Z
+
satisfying
a
f
(
n
)
+
b
f
(
n
+
1
)
+
c
f
(
n
+
2
)
<
0
af(n)+bf(n+1)+cf(n+2)<0
a
f
(
n
)
+
b
f
(
n
+
1
)
+
c
f
(
n
+
2
)
<
0
for every
n
∈
Z
+
n\in\mathbb{Z}^{+}
n
∈
Z
+
(
Z
+
\mathbb{Z}^{+}
Z
+
denotes the set of positive integers).Proposed by András Imolay, Budapest
function
algebra