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ne-nis devisible by 2 for every posilneProve thatintegere ne |
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Answer» Let n be an even positive integer.When n = 2qIn this case , we haven²- n = (2q)²- 2q = 4q²- 2q = 2q (2q - 1 )n²- n = 2r , where r = q (2q - 1)n²- n is divisible by 2 .Case ii: Let n be an odd positive integer.When n = 2q + 1In this casen²-n = (2q + 1)²- (2q + 1)= (2q +1) ( 2q+1 -1)= 2q (2q + 1)n²- n = 2r , where r = q (2q + 1)n²- n is divisible by 2.∴n²- n is divisible by 2 for every integer n |
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