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a^2+b^2+c^2 is divisible by 4 [Slovenia 2010]
a^2+b^2+c^2 is divisible by 4 [Slovenia 2010]
Source:
November 14, 2010
modular arithmetic
number theory
number theory proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive integers. Prove that
a
2
+
b
2
+
c
2
a^2+b^2+c^2
a
2
+
b
2
+
c
2
is divisible by
4
4
4
, if and only if
a
,
b
,
c
a,b,c
a
,
b
,
c
are even.
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