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Greece JBMO TST
2012 Greece JBMO TST
2
2
Part of
2012 Greece JBMO TST
Problems
(1)
p^2+2q^2+334=[p^2,q^2] , where p,q coprime
Source: Greece JBMO TST 2012 p2
4/29/2019
Find all pairs of coprime positive integers
(
p
,
q
)
(p,q)
(
p
,
q
)
such that
p
2
+
2
q
2
+
334
=
[
p
2
,
q
2
]
p^2+2q^2+334=[p^2,q^2]
p
2
+
2
q
2
+
334
=
[
p
2
,
q
2
]
where
[
p
2
,
q
2
]
[p^2,q^2]
[
p
2
,
q
2
]
is the leact common multiple of
p
2
,
q
2
p^2,q^2
p
2
,
q
2
.
number theory
least common multiple
coprime
Diophantine equation