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Regional Mathematical Olympiad
2023 India Regional Mathematical Olympiad
1
RMO 2023 P1
RMO 2023 P1
Source:
October 29, 2023
number theory
RMO 2023
Squares
Divisibility
Problem Statement
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=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}
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 abcd for all
(
a
,
b
,
c
,
d
)
∈
S
(a, b, c, d) \in S
(
a
,
b
,
c
,
d
)
∈
S
.
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