Show that the product of two consecutive even numbers is divisible by $8$ ?

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Answer 1 · 2017-03-27T10:07:31

See below.

An even number $n$ has the structure $n=2k$ where $k in ZZ$ . Now two consecutive even numbers $n, n+1$ have the structure

$(n,n+1)->(2k, 2(k+1))$ so the final relationship is

${n(n+1)=p} -> {2k(2(k+1))=p}$

or

$4k(k+1)=p$ for $k in ZZ$

NOTE: $ZZ$ denotes the set of integers. This denomination derives from the german word for integer. Zahlen.

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