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2012 Turkey Junior National Olympiad
1
1
Part of
2012 Turkey Junior National Olympiad
Problems
(1)
A diophantine equation
Source: Turkey Junior National Olympiad 2012 P1
12/12/2012
Let
x
,
y
x, y
x
,
y
be integers and
p
p
p
be a prime for which
x
2
ā
3
x
y
+
p
2
y
2
=
12
p
x^2-3xy+p^2y^2=12p
x
2
ā
3
x
y
+
p
2
y
2
=
12
p
Find all triples
(
x
,
y
,
p
)
(x,y,p)
(
x
,
y
,
p
)
.
quadratics
calculus
integration
number theory
Diophantine equation
number theory proposed