Difference between revisions of "2023 SSMO Speed Round Problems/Problem 1"
(Created page with "==Problem== Let <math>S_1 = \{2,0,3\}</math> and <math>S_2 = \{2,20,202,2023\}.</math> Find the last digit of <cmath>\sum_{a\in S_1,b\in S_2}a^b.</cmath> ==Solution== Since th...") |
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Latest revision as of 14:16, 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 .