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Question

P21 is always divisible by (if P is an odd positive integer)

A
4
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B
5
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C
6
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D
8
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Solution

The correct options are
A 4
D 8
Every odd number can be written in the form of 4k+1 or 4k+3 where k is an integer.
Case i) p=4k+1
Then p21=16k2+8k=8(2k2+k)
We see that p21 is divisible by 8 and hence also by 4.
Case ii) p=4k+3
Then p21=16k2+24k+8=8(2k2+3k+1)
We see that p21 is divisible by 8 and hence also by 4.
So in both the cases p21 is divisible by 8

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