Difference between revisions of "2024 AMC 10B Problems/Problem 7"
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~ Pi Academy | ~ Pi Academy | ||
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+ | ==Video Solution 2 by SpreadTheMathLove== | ||
+ | https://www.youtube.com/watch?v=24EZaeAThuE | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2024|ab=B|num-b=6|num-a=8}} | {{AMC10 box|year=2024|ab=B|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 13:54, 14 November 2024
Contents
[hide]Problem
What is the remainder when is divided by ?
Solution 1
We can factor the expression as
Note that is divisible by , this expression is actually divisible by 19. The answer is .
Solution 2
If you failed to realize that the expression can be factored, you might also apply modular arithmetic to solve the problem.
Since , the powers of repeat every three terms:
The fact that , , and implies that .
Video Solution 1 by Pi Academy (Fast and Easy ⚡🚀)
https://youtu.be/QLziG_2e7CY?feature=shared
~ Pi Academy
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=24EZaeAThuE
See also
2024 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.