Problem:
When p=∑k=16klnk, the number ep is an integer. What is the largest power of 2 that is a factor of ep ?
Answer Choices:
A. 212
B. 214
C. 216
D. 218
E. 220
Solution:
Because klnk=ln(kk) and the log of a product is the sum of the logs,p=ln∏k=16kk. Therefore ep is the integer 11⋅22⋅33⋅44⋅55⋅66=216⋅39⋅55, and the largest power of 2 dividing ep is 216.
The problems on this page are the property of the MAA's American Mathematics Competitions