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if a b c d are consecutive odd number then (a^2+b^2+c^2+d^2) is always divisible by?

if a b c d are consecutive odd number then (a^2+b^2+c^2+d^2) is always divisible by?

Grade:10

2 Answers

Shashank Singh
askIITians Faculty 57 Points
6 years ago
let the 4 consecutive odd numbers are (2n-3), (2n-1), (2n+1), (2n+3)
a^2+b^2+c^2+d^2= (2n-3)^2+ (2n-1)^2+(2n+1)^2+(2n+3)^2
2[(4n^2+9)+(4n^2+1)]
4(4n^2+5)
therefore it will be always be divisible by 4.
sahil
142 Points
6 years ago
it will be always divisible by to as squate of odd no is odd and thereafter sum of 4 odd is even .So sum is even and divisible by 2.

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