Difference between revisions of "2000 AMC 8 Problems/Problem 14"
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− | <cmath>-1^{19} + -1^{99} = -1 + -1 \equiv \boxed{(\ | + | <cmath>-1^{19} + -1^{99} = -1 + -1 \equiv \boxed{(\textbf{D}) \ 8} \pmod{10}</cmath> |
==See Also== | ==See Also== |
Revision as of 00:16, 12 April 2020
Contents
Problem
What is the units digit of ?
Solution
Finding a pattern for each half of the sum, even powers of have a units digit of , and odd powers of have a units digit of . So, has a units digit of .
Powers of have the exact same property, so also has a units digit of . which has a units digit of , so the answer is .
Solution 2
Using modular arithmetic:
Similarly,
We have
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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