MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Princeton University Math Competition
2022 Princeton University Math Competition
13
13
Part of
2022 Princeton University Math Competition
Problems
(1)
2022 PUMaC Team #13
Source:
9/9/2023
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
.
number theory