Problem:
The sequence is a strictly increasing arithmetic sequence of positive integers such that
What is the minimum possible value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are integers and such that . Thus . It follows that is a power of 2 ; that is, for some nonnegative integer . Then , so . Note that is the only solution (because the value of the exponential function is greater than the value of the linear function for ). Because , the pair must be one of , or . The corresponding values of are, respectively, , and 27 . The requested minimum value is .
The problems on this page are the property of the MAA's American Mathematics Competitions