Difference between revisions of "2022 SSMO Speed Round Problems/Problem 1"
Line 15: | Line 15: | ||
The expression then has the same last digit as | The expression then has the same last digit as | ||
− | + | <cmath>^2 + 2^{4} + 2^{2} + 2^{3} + 3^2 + 3^{4} + 3^{2} + 3^{3}</cmath> | |
− | |||
which is just <math>8</math>. | which is just <math>8</math>. |
Revision as of 12:41, 3 July 2023
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
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
.