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Cono Sur Olympiad
1997 Cono Sur Olympiad
3
3
Part of
1997 Cono Sur Olympiad
Problems
(1)
"Easy" number theory
Source: Cono sur Olympiad 1997 P3(Paraguai)
10/8/2017
Show that, exist infinite triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
where
a
,
b
,
c
a, b, c
a
,
b
,
c
are natural numbers, such that:
2
a
2
+
3
b
2
ā
5
c
2
=
1997
2a^2 + 3b^2 - 5c^2 = 1997
2
a
2
+
3
b
2
ā
5
c
2
=
1997
number theory
cono sur