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2018 IMO Shortlist
N5
N5
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2018 IMO Shortlist
Problems
(1)
Nice NT here
Source: IMO SL N5
7/17/2019
Four positive integers
x
,
y
,
z
x,y,z
x
,
y
,
z
and
t
t
t
satisfy the relations
x
y
ā
z
t
=
x
+
y
=
z
+
t
.
xy - zt = x + y = z + t.
x
y
ā
z
t
=
x
+
y
=
z
+
t
.
Is it possible that both
x
y
xy
x
y
and
z
t
zt
z
t
are perfect squares?
number theory
IMO Shortlist
diophantine
IMO shortlist 2018