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Problem 2
2a^4+2b^4+2c^4 square if a+b+c=0
2a^4+2b^4+2c^4 square if a+b+c=0
Source: Moldova 2000 Grade 9 P2
April 25, 2021
number theory
Problem Statement
Prove that if a,b,c are integers with
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
, then
2
a
4
+
2
b
4
+
2
c
4
2a^4+2b^4+2c^4
2
a
4
+
2
b
4
+
2
c
4
is a perfect square.
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