MathDB
Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2008 Flanders Math Olympiad
2
2
Part of
2008 Flanders Math Olympiad
Problems
(1)
1/2(a^4 +b^4 +c^4) is pefrect square if a+b+c = 0
Source: Flanders Math Olympiad 2008 p2
12/24/2022
Let
a
,
b
a, b
a
,
b
and
c
c
c
be integers such that
a
+
b
+
c
=
0
a+b+c = 0
a
+
b
+
c
=
0
. Prove that
1
2
(
a
4
+
b
4
+
c
4
)
\frac12(a^4 +b^4 +c^4)
2
1
(
a
4
+
b
4
+
c
4
)
is a perfect square.
number theory
Perfect Square