Problem:
The number 2564⋅6425 is the square of a positive integer N. In decimal representation, the sum of the digits of N is
Answer Choices:
A. 7
B. 14
C. 21
D. 28
E. 35
Solution:
We have
N=(52)64⋅(26)25=564⋅23⋅25=(5⋅2)64⋅211=1064⋅2048=204864 digits 000⋯0.
The zeros do not contribute to the sum, so the sum of the digits of N is 2+4+8=14.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions