MathDB
Problems
Contests
International Contests
Rioplatense Mathematical Olympiad, Level 3
2016 Rioplatense Mathematical Olympiad, Level 3
2
2
Part of
2016 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
\sqrt x +\sqrt y +\sqrt z=1, \sqrt{x+n} +\sqrt{y+n} +\sqrt{z+n} is an integer
Source: Rioplatense Olympiad 2016 level 3 P2
9/5/2018
Determine all positive integers
n
n
n
for which there are positive real numbers
x
,
y
x,y
x
,
y
and
z
z
z
such that
x
+
y
+
z
=
1
\sqrt x +\sqrt y +\sqrt z=1
x
+
y
+
z
=
1
and
x
+
n
+
y
+
n
+
z
+
n
\sqrt{x+n} +\sqrt{y+n} +\sqrt{z+n}
x
+
n
+
y
+
n
+
z
+
n
is an integer.
number theory
algebra
system of equations