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What is the remainder when 8^48 is divided by 63?(a) 4(b) 2(c) 1(d) 7I have been asked this question during an internship interview.My question is based upon Binomial Theorem for Positive Integral Index in division Binomial Theorem of Mathematics – Class 11

Answer»

Right option is (c) 1

The explanation is: 8^58 can be written as (8^2)^24.

8^48 = (64)^24

8^48 = (63 + 1)^24

We KNOW that (60 + 1)^24 = \(\Sigma_{r = 0}^{r = 24}\)(24Cr 63^24 – r 1^r)

= 24C0 63^24 4^0 + 24C1 63^23 4^1 +….+24C23 63^1 4^23 + 24C24 63^0 1^24

= 63 x k + 1

Therefore, the REMAINDER will be 1.



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