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Mathematics
Mathematics
Problem
Let
N
\mathbb{N}
N
be the set of all positive integers and
S
=
{
(
a
,
b
,
c
,
d
)
∈
N
4
:
a
2
+
b
2
+
c
2
=
d
2
}
S = \{(a, b, c, d) \in \mathbb{N}^4 : a^2 + b^2 + c^2 = d^2\}
S
=
{(
a
,
b
,
c
,
d
)
∈
N
4
:
a
2
+
b
2
+
c
2
=
d
2
}
. Find the largest positive integer
m
m
m
such that
m
m
m
divides
a
b
c
d
abcd
ab
c
d
for all
(
a
,
b
,
c
,
d
)
∈
S
(a, b, c, d) \in S
(
a
,
b
,
c
,
d
)
∈
S
.
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