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Cono Sur Olympiad
2024 Cono Sur Olympiad
1
Cono Sur 24/P1
Cono Sur 24/P1
Source: Cono Sur 2024
September 27, 2024
algebra
Problem Statement
Prove that there are infinitely many quadruplets of positive integers
(
a
,
b
,
c
,
d
)
(a,b,c,d)
(
a
,
b
,
c
,
d
)
, such that\\
a
b
+
1
ab+1
ab
+
1
,
b
c
+
16
bc+16
b
c
+
16
,
c
d
+
4
cd+4
c
d
+
4
,
a
d
+
9
ad+9
a
d
+
9
\\ are perfect squares
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