I have proven that if you have any 4 consecutive numbers (n, n+1, n+2, n+3) then (n+1)(n+2)=(n)(n+3)+2, but is this used for anything and if it is what is it called?
It is a special case of the formula for the sum of an arithmetic progression.
Look at Arithmetic progression - Wikipedia, the free encyclopedia
RonL
Hello, Holly!
I have proven that if you have any 4 consecutive numbers (n, n+1, n+2, n+3)
then (n+1)(n+2) = (n)(n+3)+2, but is this used for anything
and if it is, what is it called?
With four consecutive numbers, the product of the "inner two"
. . is always 2 greater than the product of the "outer two".
As far as I know, this does not have a name nor a particular use.
. . But it is an interesting fact.
A similar phenomenon:
If two integers differ by 2, their product is one less than a perfect square.
Examples: .7 x 9 .= . 63 . = . 8² - 1
. . . . . . .12 x 14 .= .168 .= .13² - 1
This is glaringly obvious when we see: .(n - 1)(n + 1) .= .n² - 1