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India Pre-Regional Mathematical Olympiad
2012 India PRMO
16
2012 preRMO p16, \Sigma_{k=1}^{20}f(k)
2012 preRMO p16, \Sigma_{k=1}^{20}f(k)
Source:
June 17, 2019
algebra
Sum
function
Problem Statement
Let
N
N
N
be the set of natural numbers. Suppose
f
:
N
→
N
f: N \to N
f
:
N
→
N
is a function satisfying the following conditions: (a)
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn) =f(m)f(n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
(b)
f
(
m
)
<
f
(
n
)
f(m) < f(n)
f
(
m
)
<
f
(
n
)
if
m
<
n
m < n
m
<
n
(c)
f
(
2
)
=
2
f(2) = 2
f
(
2
)
=
2
What is the sum of
Σ
k
=
1
20
f
(
k
)
\Sigma_{k=1}^{20}f(k)
Σ
k
=
1
20
f
(
k
)
?
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