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13
2022 PUMaC Team #13
2022 PUMaC Team #13
Source:
September 9, 2023
number theory
Problem Statement
Of all functions
h
:
Z
>
0
→
Z
≥
0
h : Z_{>0} \to Z_{\ge 0}
h
:
Z
>
0
→
Z
≥
0
, choose one satisfying
h
(
a
b
)
=
a
h
(
b
)
+
b
h
(
a
)
h(ab) = ah(b) + bh(a)
h
(
ab
)
=
ah
(
b
)
+
bh
(
a
)
for all
a
,
b
∈
Z
>
0
a, b \in Z_{>0}
a
,
b
∈
Z
>
0
and
h
(
p
)
=
p
h(p) = p
h
(
p
)
=
p
for all prime numbers
p
p
p
. Find the sum of all positive integers
n
≤
100
n\le 100
n
≤
100
such that
h
(
n
)
=
4
n
h(n) = 4n
h
(
n
)
=
4
n
.
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