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2003 Unirea
2003 Unirea
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(1)
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27 elements
Let
K
\displaystyle \mathcal K
K
be a field with
27
\displaystyle 27
27
elements. Prove that there is
a
∈
K
\displaystyle a \in \mathcal K
a
∈
K
such that
a
3
=
a
+
2
\displaystyle a^3 = a + 2
a
3
=
a
+
2
. Mircea Becheanu