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Putnam
1955 Putnam
B6
B6
Part of
1955 Putnam
Problems
(1)
Putnam 1955 B6
Source:
5/24/2022
Prove: If
f
(
x
)
>
0
f(x) > 0
f
(
x
)
>
0
for all
x
x
x
and
f
(
x
)
→
0
f(x) \rightarrow 0
f
(
x
)
→
0
as
x
→
∞
,
x \rightarrow \infty,
x
→
∞
,
then there exists at most a finite number of solutions of
f
(
m
)
+
f
(
n
)
+
f
(
p
)
=
1
f(m) + f(n) + f(p) = 1
f
(
m
)
+
f
(
n
)
+
f
(
p
)
=
1
in positive integers
m
,
n
,
m, n,
m
,
n
,
and
p
.
p.
p
.
Putnam