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.
This Question Belongs to Arithmetic Ability >> Number System
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