MathDB
Problems
Contests
International Contests
IMO Shortlist
2018 IMO Shortlist
N5
Nice NT here
Nice NT here
Source: IMO SL N5
July 17, 2019
number theory
IMO Shortlist
diophantine
IMO shortlist 2018
Problem Statement
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?
Back to Problems
View on AoPS