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Putnam
1997 Putnam
3
Putnam 1997 B3
Putnam 1997 B3
Source:
May 30, 2014
Putnam
number theory
greatest common divisor
college contests
Problem Statement
For each positive integer
n
n
n
write the sum
∑
i
=
n
1
i
=
p
n
q
n
\sum_{i=}^{n}\frac{1}{i}=\frac{p_n}{q_n}
∑
i
=
n
i
1
=
q
n
p
n
with
gcd
(
p
n
,
q
n
)
=
1
\text{gcd}(p_n,q_n)=1
gcd
(
p
n
,
q
n
)
=
1
. Find all such
n
n
n
such that
5
∤
q
n
5\nmid q_n
5
∤
q
n
.
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