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Show 6 divides (n^2+5)n
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dextercioby
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6
Jan15-11, 10:06 AM
Sci Advisor
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P: 11,894
You can prove it without mathematical induction, too
[tex] k\left(k^2 +5\right) =k\left[(k+1)(k+2)-3k+3\right]= k(k+1)(k+2)-3k(k-1) [/tex]
which is obviously divisible by 6.