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2009 IMAR Test
1
1
Part of
2009 IMAR Test
Problems
(1)
diophantine system xy +zw = a, xz + yw = b has finitely solutions x,y,z,w
Source: IMAR 2009 p1
9/27/2018
Given
a
a
a
and
b
b
b
distinct positive integers, show that the system of equations
x
y
+
z
w
=
a
x y +zw = a
x
y
+
z
w
=
a
x
z
+
y
w
=
b
xz + yw = b
x
z
+
y
w
=
b
has only finitely many solutions in integers
x
,
y
,
z
,
w
x, y, z,w
x
,
y
,
z
,
w
.
Diophantine equation
algebra
number theory
system of equations