Problem:
How many of the first ten numbers of the sequence 121,11211,1112111,… are prime numbers?
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
Note that
121112111112111​=110+11=11⋅(10+1),=11100+111=111⋅(100+1),=1111000+1111=1111⋅(1000+1),​
and so on. Therefore each number in the sequence can be written as a product of two positive integers, each greater than 1 , so none of the numbers in this sequence is prime.
The problems on this page are the property of the MAA's American Mathematics Competitions