Difference between revisions of "2016 AMC 8 Problems/Problem 15"
m |
Hashtagmath (talk | contribs) |
||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
What is the largest power of <math>2</math> that is a divisor of <math>13^4 - 11^4</math>? | What is the largest power of <math>2</math> that is a divisor of <math>13^4 - 11^4</math>? | ||
Revision as of 02:56, 16 January 2021
Problem
What is the largest power of 
that is a divisor of 
?
Solution
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 
.
| 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. 
