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
Answer: c
Explanation: 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.
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.
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