Question

$QUESTION$

if n is an odd integer then show that n²-1 is divisible by (8)



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Answer 1

Answer:

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if n is an odd integer then show that n²-1 is divisible by (8)

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Refer to the attachment

Answer 2

Answer:

Any +ve odd integer is of the form 4q + 1 or 4q + 3 for some integer ( q ) so if ( n ) = 4q + 1

N² - 1 = ( 4q + 1 ) ² - 1 = 16q² + 8q = 8q ( 2q + 1 ) => n² - 1 is divisible by 8 .

If n = 4q + 3

n² - 1 => ( 4q + 3 ) ² - 1 = 16q² + 24q + 8 = 8 ( 2q² + 3q + 1 ) => n² - 1 is divisible by 8 .