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5
An indeterminate equation
An indeterminate equation
Source: 2013 Taiwan TST
July 12, 2015
number theory
Taiwan
Taiwan TST 2013
Problem Statement
If
x
,
y
,
z
x,y,z
x
,
y
,
z
are positive integers and
z
(
x
z
+
1
)
2
=
(
5
z
+
2
y
)
(
2
z
+
y
)
z(xz+1)^2=(5z+2y)(2z+y)
z
(
x
z
+
1
)
2
=
(
5
z
+
2
y
)
(
2
z
+
y
)
, prove that
z
z
z
is an odd perfect square.
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