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Turkey Team Selection Test
2003 Turkey Team Selection Test
4
4
Part of
2003 Turkey Team Selection Test
Problems
(1)
(x^2+y^2)^2 + 2tx(x^2 + y^2) = t^2y^2
Source: Turkey TST 2003 - P4
4/6/2013
Find the leasta. positive real numberb. positive integer
t
t
t
such that the equation
(
x
2
+
y
2
)
2
+
2
t
x
(
x
2
+
y
2
)
=
t
2
y
2
(x^2+y^2)^2 + 2tx(x^2 + y^2) = t^2y^2
(
x
2
+
y
2
)
2
+
2
t
x
(
x
2
+
y
2
)
=
t
2
y
2
has a solution where
x
,
y
x,y
x
,
y
are positive integers.
function
algebra proposed
algebra
number theory