- #1
Terry Coates
- 39
- 2
A SURPRISING DISCOVERY:
I have only recently discovered the following equations of a certain function of a pair of two integers, which surprised me:-
f(x, y) = {f(x+z, y+z) + f(x-z, y-z)}/2 ----------------1
f(x, y) = {f(x+1, y+1) + f(x-1, y-1)}/2-2 .-----------------2
Where z = any value, positive or negative.
Of course the first equation is true for f(x,y) = x+/-y, and the second is true for f(x,y) = x+/-y-2, but there is another surprising function (non linear) which I will leave the reader to discover for now.
I have only recently discovered the following equations of a certain function of a pair of two integers, which surprised me:-
f(x, y) = {f(x+z, y+z) + f(x-z, y-z)}/2 ----------------1
f(x, y) = {f(x+1, y+1) + f(x-1, y-1)}/2-2 .-----------------2
Where z = any value, positive or negative.
Of course the first equation is true for f(x,y) = x+/-y, and the second is true for f(x,y) = x+/-y-2, but there is another surprising function (non linear) which I will leave the reader to discover for now.