If we take enough consecutive integer base numbers and raise them to the same power, we have (for example):
If we then subtract these numbers orderly, pair by pair, we get another vertical row of numbers, but now there is one number less than in original series (5 versus 6 numbers):
If we repeat this process, we get:
So, in this example the end-point is 24.
Had we chosen initial raising number to be 3, the end point would be 6. With raising number 2 it would be 2 and with raising number 5 we should have 120 as the end point.
So, the rule appears to be: with raising number x we end to factorial of x.
Can anyone tell me, what is the NAME OF THIS METHOD??? (not just this example-method which produces factorials, but this pair by pair subtraction method in general).
I am very interested in this method, but have difficulties to find more information of it from internet and even from this math help forum.
I have only found one name for it (from John H Conway & Richard K Guys book "The Book of Numbers" from 1996, pages 79-89). They gave it name "difference table".
However, when I try this term in search-engines, I only find information of calculus, differentiation etc.
Please, help me!