Problem: Find a positive integral solution to the equation
2+4+6+⋯+2n1+3+5+⋯+(2n−1)=116115.
Answer Choices:
A. 110
B. 115
C. 116
D. 231
E. The equation has no positive integral solutions.
Solution:
Sumbing the arithmetic progressions yields
116115=2+4+⋯+2n1+3+⋯+(2n−1)=n(n+1)n2;116115=n+1n;n=115.