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Oliveboard Question of the day

Given that ap = 2p´x 3p + 23p – 2.

What is the remainder when a98 is divided by 98?

a. 1
b. 97
c. 0
d. 96

Answers and Explanations

Answer: (3)

Solution:

We can reduce the equation to a simplified form:

ap= 2p(3p+ 22p – 21-p)

= 2p´3p + 23p – 2

= 6p + 8[ – 2

= (7-1)p + (7+1)p – 2

= 2(7p + pc2 7p-2 +…….+ 1) – 2

= 98b + 2 – 2 where b is any natural number

= 98b

Hence, the remainder is 0.

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