Question

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Answer 1

we know,

odd number in the form of (2P+1 where P is a natural number,

so,n²-1=(2P+1)²-1

=4P²+40+1-1

=4P²+4P

now, checking:

p=1 then,

4P²+4P=4(1)²+4(1)=4+4=8, it is divisible by 8.

P=2 then,

4P²+4P=4(2)²+4(2)=16+8=24, it is also divisible by 8.

P=2 then,

4P²+4P=4(3)²+4(3)=36+12=48, divisible by 8.

Hence, we conclude that 4P²+4P is divisible by 8 for all natural number . hence, n²-1 is divisible by 8 for all odd blue of n.

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