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2024 Japan MO Finals
5
Simple NT
Simple NT
Source: 2024 Japan MO P5
February 11, 2024
number theory
Problem Statement
Prove that there are no pairs of positive integers
(
a
,
b
,
c
,
d
,
n
)
(a,b,c,d,n)
(
a
,
b
,
c
,
d
,
n
)
such that
a
2
+
b
2
+
c
2
+
d
2
−
4
a
b
c
d
=
7
⋅
2
2
n
−
1
.
a^2+b^2+c^2+d^2-4\sqrt{abcd}=7\cdot 2^{2n-1}.
a
2
+
b
2
+
c
2
+
d
2
−
4
ab
c
d
=
7
⋅
2
2
n
−
1
.
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