prove that n^2 -1 where n isodd integer which is divisible by 8
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We know that any odd positive integer is of the form 4q+1 and 4q+3
Case 1
N=4q+1
N^2-1=(4q+1)^2-1
=16q^2 +8q +1 -1
8(8q^2+q)
Therefore it is divisible by 8
Case 2
N=4q+3
N^2-1=(4q+3)^2
=16q^2 + 24q +9-1
=8(8q^2 +3q+1)
Therefore again it is divisible by 8
Hence proved
Hope this helps make as brainliest
Case 1
N=4q+1
N^2-1=(4q+1)^2-1
=16q^2 +8q +1 -1
8(8q^2+q)
Therefore it is divisible by 8
Case 2
N=4q+3
N^2-1=(4q+3)^2
=16q^2 + 24q +9-1
=8(8q^2 +3q+1)
Therefore again it is divisible by 8
Hence proved
Hope this helps make as brainliest
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