Dear Mr. Dr. Peterson!

Thank you!

Now, if I don't forget the n, then it's correct.

Well, I tried to do it like you did, so with all the digits of 96433469 and not only 3469.

But then, my function is different. Here is my work:

9

///6

///4

///3

///3

///4

///6

///9

/-3

//-2

//-1

///0

///1

///2

///3

////1

///1

///1

///1

///1

///1

a+b+c

///4a+2b+c

///9a+3b+c

///16a+4b+c

///25a+5b+c

///36a+6b+c

///49a+7b+c

///64a+8b+c

/////3a+b

////////5a+b

///////7a+b

/////////9a+b

////////11a+b

///////13a+b

////////15a+b

/////////////2a

///////////2a

///////////2a

///////////2a

/////////////2a

/////////////2a

F

= an^2 + bn + c

3.row:

a=0,5 because of 2a=1

a=0,5 because of 2a=1

2.row:

b=-4,5 because of 3a+b=-3 and a=0,5

b=-4,5 because of 5a+b=-2 and a=0,5

b=-4,5 because of 7a+b=-1 and a=0,5

b=-4,5 because of 9a+b=0 and a=0,5

b=-4,5 because of 11a+b=1 and a=0,5

b=-4,5 because of 13a+b=2 and a=0,5

b=-4,5 because of 15a+b=3 and a=0,5

1.row:

c=13 because of a+b+c=9 and a=0,5 and b=-4,5

c=13 because of 4a+2b+c=6 and a=0,5 and b=-4,5

c=13 because of 9a+3b+c=4 and a=0,5 and b=-4,5

c=13 because of 16a+4b+c=3 and a=0,5 and b=-4,5

c=13 because of 25a+5b+c=3 and a=0,5 and b=-4,5

c=13 because of 36a+6b+c=4 and a=0,5 and b=-4,5

c=13 because of 49a+7b+c=6 and a=0,5 and b=-4,5

c=13 because of 64a+8b+c=9 and a=0,5 and b=-4,5

F

= an^2 + bn + c

F

= 0,5n^2 - 4,5n + 13

F(1)=0,5-4,5+13=9

F(2)=0,5x4-9+13=6

F(3)=0,5x9-13,5+13=4

F(4)=0,5x16-18+13=3

F(5)=0,5x25-22,5+13=3

F(6)=0,5x36-27+13=4

F(7)=0,5x49-31,5+13=6

F(8)=0,5x64-36+13=9

My function is F

= 0,5n^2 - 4,5n +13

Could you please explain me why I've got a different function for n?

Where's my mistake?

I've got another question. I still didn't really understand what the function prooves more than the explaination with the digits?