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PEN A Problems
100
A 100
A 100
Source:
May 25, 2007
calculus
integration
modular arithmetic
Divisibility Theory
Problem Statement
Find all positive integers
n
n
n
such that
n
n
n
has exactly
6
6
6
positive divisors
1
<
d
1
<
d
2
<
d
3
<
d
4
<
n
1<d_{1}<d_{2}<d_{3}<d_{4}<n
1
<
d
1
<
d
2
<
d
3
<
d
4
<
n
and
1
+
n
=
5
(
d
1
+
d
2
+
d
3
+
d
4
)
1+n=5(d_{1}+d_{2}+d_{3}+d_{4})
1
+
n
=
5
(
d
1
+
d
2
+
d
3
+
d
4
)
.
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