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.
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.
-
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.
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.