2022 SSMO Speed Round Problems/Problem 1
Problem
Let and
Find the last digit of
Solution
Since the power of to an integer is always
, it
follows that we want to find the last digit of
\end{align*}
Since the powers of
are
it follows that
and
have the same last
digit for
. Similarily,
and
have the same last digit. (This follows as
too).
The expression then has the same last digit as
which is just
.