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.