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IMC
1999 IMC
1
Trivial
Trivial
Source: IMC 1999 day 2 problem 1
November 19, 2005
superior algebra
superior algebra solved
Problem Statement
Let
R
R
R
be a ring where
∀
a
∈
R
:
a
2
=
0
\forall a\in R: a^2=0
∀
a
∈
R
:
a
2
=
0
. Prove that
a
b
c
+
a
b
c
=
0
abc+abc=0
ab
c
+
ab
c
=
0
for all
a
,
b
,
c
∈
R
a,b,c\in R
a
,
b
,
c
∈
R
.
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