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Rioplatense Mathematical Olympiad, Level 3
2023 Rioplatense Mathematical Olympiad
1
Mixing squares with prime
Mixing squares with prime
Source: Rioplatense L3 2023 #1
December 6, 2023
number theory
Problem Statement
Determine all triples
(
x
,
y
,
p
)
(x,y,p)
(
x
,
y
,
p
)
of positive integers such that
p
p
p
is prime,
p
=
x
2
+
1
p=x^2+1
p
=
x
2
+
1
and
2
p
2
=
y
2
+
1
2p^2=y^2+1
2
p
2
=
y
2
+
1
.
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