Hello.

If we take enough consecutive integer base numbers and raise them to the same power, we have (for example):

1^4=1

2^4=16

3^4=81

4^4=256

5^4=625

6^4=1296

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):

16-1=15

81-16=65

256-81=175

625-256=369

1296-625=671

If we repeat this process, we get:

65-15=50

175-65=110

369-175=194

671-369=302

...and...

110-50=60

194-110=84

302-194=108

...and...

84-60=24

108-84=24

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!