Let
and
be disjoint nonempty sets with
. Show that there exist elements
and
such that the number
is divisible by
.
%V0
Let $A$ and $B$ be disjoint nonempty sets with $A \cup B = \{1, 2,3, \ldots, 10\}$. Show that there exist elements $a \in A$ and $b \in B$ such that the number $a^3 + ab^2 + b^3$ is divisible by $11$.
Školjka