How do you prove this statement holds
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How do you prove this statement holds

[From: ] [author: ] [Date: 13-08-22] [Hit: ]
then it is obviously true.If n is not divisible by 3 then n=3k+1 or n=3k+2 for some integer k.If n=3k+1, then 2n+1 = 2(3k+1) +1 = 6k+3.........
Don't even know where to start, hate argument question n have an exam coming up. Please explain

3 | n(2n + 1)(4n + 1) for any integer n

Further explanation : n(2n + 1)(4n + 1) for any integer n, is a factor of 3.

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Well, if n is divisible by 3, then it is obviously true.

If n is not divisible by 3 then n=3k+1 or n=3k+2 for some integer k.

If n=3k+1, then 2n+1 = 2(3k+1) +1 = 6k+3... is divisible by 3.

If n=3k+2, then 4n+1 = 4(3k+2)+1 = 12k+9... is divisible by 3.
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