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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
98
98
Part of
PEN A Problems
Problems
(1)
A 98
Source:
5/25/2007
Let
n
n
n
be a positive integer with
k
≥
22
k\ge22
k
≥
22
divisors
1
=
d
1
<
d
2
<
⋯
<
d
k
=
n
1=d_{1}< d_{2}< \cdots < d_{k}=n
1
=
d
1
<
d
2
<
⋯
<
d
k
=
n
, all different. Determine all
n
n
n
such that
d
7
2
+
d
10
2
=
(
n
d
22
)
2
.
{d_{7}}^{2}+{d_{10}}^{2}= \left( \frac{n}{d_{22}}\right)^{2}.
d
7
2
+
d
10
2
=
(
d
22
n
)
2
.
Divisibility Theory