Difference between revisions of "2014 AMC 10B Problems/Problem 17"
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==Solution== | ==Solution== | ||
| − | We begin by factoring the <math>2^ | + | We begin by factoring the <math>2^{1002}</math> out. This leaves us with <math>5^{1002} - 1</math> This gives us the final answer of <math>\textbf{(D) } 2^{1005}</math>. |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2014|ab=B|num-b=16|num-a=18}} | {{AMC10 box|year=2014|ab=B|num-b=16|num-a=18}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:56, 20 February 2014
Problem 17
What is the greatest power of 
that is a factor of 
?
Solution
We begin by factoring the 
out. This leaves us with 
This gives us the final answer of 
.
See Also
| 2014 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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. 
