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South Africa Contests
South Africa National Olympiad
2012 South africa National Olympiad
6
6
Part of
2012 South africa National Olympiad
Problems
(1)
Functional inequality
Source: SAMO Senior Round 3 2012 Problem 6
9/6/2012
Find all functions
f
:
N
→
R
f:\mathbb{N}\to\mathbb{R}
f
:
N
→
R
such that
f
(
k
m
)
+
f
(
k
n
)
−
f
(
k
)
f
(
m
n
)
≥
1
f(km)+f(kn)-f(k)f(mn)\ge 1
f
(
km
)
+
f
(
kn
)
−
f
(
k
)
f
(
mn
)
≥
1
for all
k
,
m
,
n
∈
N
k,m,n\in\mathbb{N}
k
,
m
,
n
∈
N
.
inequalities
function
limit
algebra unsolved
algebra