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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
110
110
Part of
PEN A Problems
Problems
(1)
A 110
Source:
5/25/2007
For each positive integer
n
n
n
, write the sum
∑
m
=
1
n
1
/
m
\sum_{m=1}^n 1/m
∑
m
=
1
n
1/
m
in the form
p
n
/
q
n
p_n/q_n
p
n
/
q
n
, where
p
n
p_n
p
n
and
q
n
q_n
q
n
are relatively prime positive integers. Determine all
n
n
n
such that 5 does not divide
q
n
q_n
q
n
.
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number theory
relatively prime
Divisibility Theory