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For any integer n , n^2 + 5 is not divisible by 4 ?

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  • For any integer n , n^2 + 5 is not divisible by 4 ?


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Answer #1 | 23/07 2014 11:45
if n is an even number : (2n)^2 + 5 = 4n^2 + 5 if n is an odd number : (2n+1)^2 + 5 = 4n^2 + 4n + 6 you can't factor "4" => n^2 + 5 is not divisible by 4
Answer #2 | 23/07 2014 11:44
assume n^2 + 5 is divisible by 4 thus n^2 + 5 = 0 (mod 4) n^2 = -1 (mod 4) = 3 (mod 4) n^2 = 7 (mod 4) = 11 (mod 4) all is impossible, thus a contradiction so n^2 + 5 not = 0 (mod 4 )

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