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PEN K Problems
14
K 14
K 14
Source:
May 25, 2007
function
inequalities
Functional Equations
Problem Statement
Find all functions
f
:
Z
→
Z
f:\mathbb{Z} \to \mathbb{Z}
f
:
Z
→
Z
such that for all
m
∈
Z
m\in\mathbb{Z}
m
∈
Z
: [*]
f
(
m
+
8
)
≤
f
(
m
)
+
8
f(m+8) \le f(m)+8
f
(
m
+
8
)
≤
f
(
m
)
+
8
, [*]
f
(
m
+
11
)
≥
f
(
m
)
+
11
f(m+11) \ge f(m)+11
f
(
m
+
11
)
≥
f
(
m
)
+
11
.
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