Difference between revisions of "2016 AMC 8 Problems/Problem 15"
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+ | What is the largest power of <math>2</math> that is a divisor of <math>13^4 - 11^4</math>? | ||
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+ | <math>\textbf{(A)}\mbox{ }8\qquad \textbf{(B)}\mbox{ }16\qquad \textbf{(C)}\mbox{ }32\qquad \textbf{(D)}\mbox{ }64\qquad \textbf{(E)}\mbox{ }128</math> | ||
==Solution 1== | ==Solution 1== | ||
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~CHECKMATE2021 | ~CHECKMATE2021 | ||
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== Video Solution by OmegaLearn== | == Video Solution by OmegaLearn== |
Latest revision as of 21:58, 17 May 2024
Contents
[hide]Problem
What is the largest power of that is a divisor of ?
Solution 1
First, we use difference of squares on to get . Using difference of squares again and simplifying, we get . Realizing that we don't need the right-hand side because it doesn't contain any factor of 2, we see that the greatest power of that is a divisor is .
~CHECKMATE2021
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=3705
~ pi_is_3.14
Video Solution
~savannahsolver
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.