If a, b, and c are consecutive integers, then a= n, b= n+1, c= n+ 2 for some integer n and so so, first of all, must be divisible by 3. But 3 is prime so d must be divisible by 3, d= 3m and so : and then
Hi everyone. (This is my first post here)
Where can I find an ordered list of primitive equations of the form:
where are consecutive numbers.
Or alternatively, can anyone give me a formula to produce a list of such equations?
Do these equations have a name? The similar situation in squares are called "Pythagorean Triplets". But I'm not familiar with any name associated with this similar form in cubes. If they have a specific name I could probably just type that into Google.
Thank you for your precious time.
If a, b, and c are consecutive integers, then a= n, b= n+1, c= n+ 2 for some integer n and so so, first of all, must be divisible by 3. But 3 is prime so d must be divisible by 3, d= 3m and so : and then
Thank you very much!
I think you meant though.
You actually typed
But I see the big picture now.
I thought that would be an easy calculation.
But now how do I go about finding m & n's that are whole number solutions to that equation?
I'm seeking a quick way to generate a list of these consecutive equations.
When I type this into spreadsheet and chose an arbitrary n I get solutions for m that aren't whole numbers, or vice versa.
I would settle for a list on the Internet of these consecutive equations if someone knows where I can find such a list.
Surely these must have been calculated by someone at some point in time.
Let's see if we can whittle this down a bit more.
has solutions n = 3, 4, and 8 (mod 9).
Let's take n = 9p + 3, for all p.
Then the equation becomes
One immediate solution of this is p = 0, m = 2. (a = 3, b = 4, c = 5, d = 6). p obviously can't be negative. I checked up to p = 25 and could not find any more solutions. I can't think of a way to get closer than this.
I'll let you work out n = 4, 8 (mod 9).
-Dan
Edit: Unless I programmed Excel wrong, there are no solutions up to p = 1000 in any of the three categories except for the one mentioned above. I suspect that's the only one.