The highest power of 17 which can divide exactly the following:
(18² - 1) (18⁴ - 1) (18⁶ - 1) (18⁸ - 1) . . . . (18¹⁶ - 1) (18¹⁸ - 1) is :

A. 1

B. 17

C. 9

D. 13

E. Cannot determined

Answer: Option C

Solution(By Examveda Team)

Total number of terms in expression = 9
(18² - 1) = (18 - 1) × (18 + 1)
(18⁴ - 1) = (18² + 1) × (18² - 1) = (18² + 1) × (18 - 1) × (18 + 1)
(18⁶ - 1) = [(18³)² -1] = (18³ + 1) (18³ - 1) = 17 × k and so on.
Hence, there will be 9 times 17 in the whole expression as each term of expression gives one 17. Therefore for maximum power of 17 will be 9.