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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
68
68
Part of
PEN H Problems
Problems
(1)
H 68
Source:
5/25/2007
Consider the system
x
+
y
=
z
+
u
,
x+y=z+u,
x
+
y
=
z
+
u
,
2
x
y
=
z
u
.
2xy=zu.
2
x
y
=
z
u
.
Find the greatest value of the real constant
m
m
m
such that
m
≤
x
y
m \le \frac{x}{y}
m
≤
y
x
for any positive integer solution
(
x
,
y
,
z
,
u
)
(x, y, z, u)
(
x
,
y
,
z
,
u
)
of the system, with
x
≥
y
x \ge y
x
≥
y
.
ratio
calculus
Diophantine Equations