Number System Practice Test 5

Question : 7 of 40

Marks: +1, -0

Find the remainder when

(23)^142

is divided by 24.

Solution:

(23)^142=[(23)^142-1]+1

=[(23)^142-(1)^142]+1

{a^n-b^n}

is divisible by (a + b) if n is even.
So,

[(23)^142-(1)^142]

is divisible by (23 + 1) = 24.
So, remainder is 1.

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