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How to prove the sum of the squares of 5 consecutive numbers is divisible by 5 (question gives you numbers)?

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Prove that the sum of the squares of 5 consecutive numbers is divisible by 5.

Begin by writing the middle number as n, so that the other numbers are n-2, n-1, n +1, n+2

How would I prove this? I tried to but ended with n^10 x 10 and didn't know if that's even divisble by 5 or how it to say it divides by 5

Any help greatly appreciated! 10pts will be given out

Answers (3)

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qvufpxgwaa profile image
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aa10395375 profile image

x²+(x+1)²+(x+2)²+(x+3)²+(x+4)²= 5x²+20x+30= 5(x²+4x+6)

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ehyccuwxaa profile image

start with n

(n)+(n+1)(n+2)(n+3)(n+4)(n+5)

5n+15

5(n+3)

which is divisible by 5