Re: While shifting his departmental store, Mr. Johnson found the number of
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07 Aug 2023, 22:43
OE
The number of articles in the store was 7^{20} which were stored in 8 rooms of equal capacity. As 𝑛 articles were left with no space in the room, hence the minimum value of 𝑛 will be the remainder we get when 7^{20} is divided by 8
n= the remainder of \(\frac{7^{20}}{8}\)
dividing \(7^1\) by 8 the remainder is 7
\(7^2\) by 8 we have a remainder of 1
So we do have a ciclicity
Dividing the odd powers of 7 by 8 gives us a remainder 7 whereas dividing even powers of 7 by 8 gives us a remainder 1.
Now, we need to find the remainder when \(7^{20}\) is divided by 8.
Since, the power is even, the remainder will be 1.
Hence, the answer is B.
Ans.(B)