Something I have come across recently ...

Take the Fibonacci sequence ( 1,1,2,3,5,8,13,21,...) and us it as coeff. for linear simultaneous equations:

For example

x+y =2

3x+5y=8

OR

2x+3y=5

8x+13y=21

These simultaneous equations and any others formed in the same way, have the same solution

I know its possible to see that x=1, y=1 and perhaps quite obvious..

Are there other sequences we can use in the same that might give the same solutions every time?