Really cool thing with the numbers like a^x

krisper · 2006-01-14 05:37:40

Here is what we do:
1. We have the numbers from 1 to 10 a∈{1,2,3,4,5,6,7,8,9,10}.
2. x is the power of these numbers.
3. Take any random integer number x that is between 0 and +∞.
4. Calculate
1^x = b1
2^x = b2
3^x = b3
4^x = b4
5^x = b5
6^x = b6
7^x = b7
8^x = b8
9^x = b9
10^x = b10
5. Now the fun part We calculate this:
c1 = b2 - b1;
c2 = b3 - b2;
c3 = b4 - b3;
c4 = b5 - b4;
c5 = b6 - b5;
c6 = b7 - b6;
c7 = b8 - b7;
c8 = b9 - b8;
c9 = b10 - b9;
6. Now we have the set of numbers c1..c9. We do the same and get the set d1..d8 (d1 = c2 - c1, d2 = c3 - c2 and etc.). We do this until we get a set of numbers that has equal numbers and if we decide to subtract again we will get 0. These equal numbers we will call Z.
7. Write here what value of x have you used and what Z have you got as answer?

P.S.
If all your calculations are correct you will have a Z that equals x!

Last edited by krisper (2006-01-14 08:47:46)

mathsyperson · 2006-01-14 06:06:29

That only works when x is a positive integer.

It's a nice pattern though. I played around with it, and discovered that you need to do Step 4. x times before you get your Z value. Also, if you're doing high values of x, you'll need more than 10 numbers to start off with.

Last edited by mathsyperson (2006-01-14 11:28:29)

krisper · 2006-01-14 07:12:52

Thanks for your reply mathsyperson.

And yes, you are correct and that why I said that x should be >=0 By the way I found this on my own a couple of years ago when I was playing of numbers hoping I will find something significant (everyone's dream ). It is very nice though, because when repeating the steps you will always get to the 0 value.

mathsyperson · 2006-01-14 07:31:17

It doesn't work with x=0 either. For that, you get a Z value of 1.
And my main point in the previous post was that x had to be an integer. If you take it as √ 2, then you'll get all kinds of odd numbers. They won't ever reach 0 either. At least, I don't think they will.

krisper · 2006-01-14 08:20:36

When is 0 you will get Z=1 and 0! equals 1, so n can be 0 And you are right again, it is only for integers because n! formula can only be used for integers that are >=0.

P.S. I have edited my first post telling that x must be integer

Last edited by krisper (2006-01-14 08:48:45)

MathsIsFun · 2006-01-14 10:45:52

From Excel:

		
x=4		
		
 1	    1					
 2	   16	  15				
 3	   81	  65	 50			
 4	  256	 175	110	 60		
 5	  625	 369	194	 84	24	
 6	 1296	 671	302	108	24	0
 7	 2401	1105	434	132	24	0
 8	 4096	1695	590	156	24	0
 9	 6561	2465	770	180	24	0
10	10000	3439	974	204	24	0

And for x=5 you need an extra column to reach 0

And it is fun to play with real values of x

mathsyperson · 2006-01-14 11:31:08

krisper wrote:

When is 0 you will get Z=1 and 0! equals 1, so n can be 0

Oh! Sorry! When I read your original thing about Z=x!, I inferred that that was an exclamation mark, but now after reading MathsIsFun's post I realise that it was actually a factorial sign. Sorry again!

Math Is Fun Forum

#1 2006-01-14 05:37:40

Really cool thing with the numbers like a^x

#2 2006-01-14 06:06:29

Re: Really cool thing with the numbers like a^x

#3 2006-01-14 07:12:52

Re: Really cool thing with the numbers like a^x

#4 2006-01-14 07:31:17

Re: Really cool thing with the numbers like a^x

#5 2006-01-14 08:20:36

Re: Really cool thing with the numbers like a^x

#6 2006-01-14 10:45:52

Re: Really cool thing with the numbers like a^x

#7 2006-01-14 11:31:08

Re: Really cool thing with the numbers like a^x

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