MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Romania National Olympiad
2004 Romania National Olympiad
1
Natural numbers
Natural numbers
Source: RMO 2004, Grade 8, Problem 1
February 26, 2006
Problem Statement
Find all non-negative integers
n
n
n
such that there are
a
,
b
ā
Z
a,b \in \mathbb Z
a
,
b
ā
Z
satisfying
n
2
=
a
+
b
n^2=a+b
n
2
=
a
+
b
and
n
3
=
a
2
+
b
2
n^3=a^2+b^2
n
3
=
a
2
+
b
2
. Lucian Dragomir
Back to Problems
View on AoPS