?
The highest power of 17 which can divide exactly the following:
The highest power of 17 which can divide exactly the following:
(182 - 1) (184 - 1) (186 - 1) (188 - 1) . . . . (1816 - 1) (1818 - 1) is :
Answer & Solution
Correct Answer:
Option
C
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.
(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.
Join the Discussion
Login to post a comment or share your explanation.
Login