Problem:
What is the largest power of 2 that is a divisor of 134−114?
Answer Choices:
A. 8
B. 16
C. 32
D. 64
E. 128
Solution:
Factor, using a difference of two squares:
134−114=(132+112)(13+11)(13−11)=290⋅24⋅2=2⋅145⋅8⋅3⋅2=32⋅435
So the largest power of 2 that is a divisor of 134−114 is 32.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions