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)