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PEN F Problems
14
F 14
F 14
Source:
May 25, 2007
rational numbers
Problem Statement
Let
k
k
k
and
m
m
m
be positive integers. Show that
S
(
m
,
k
)
=
∑
n
=
1
∞
1
n
(
m
n
+
k
)
S(m, k)=\sum_{n=1}^{\infty}\frac{1}{n(mn+k)}
S
(
m
,
k
)
=
n
=
1
∑
∞
n
(
mn
+
k
)
1
is rational if and only if
m
m
m
divides
k
k
k
.
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