[seqfan] Fibonacci sequences sharing no terms

[Eric Angelini]

Hello Seqfans,
please forgive me if this question is naïve.
Consider Fib(1,2) = 1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,...
Now will Fib(4,6) = 4,6,10,16,26,42,68,110,178,288,466,... share at some point
one term (or more) with Fib(1,2)?
If yes or no, do we know why? Are there constraints on 'a' and 'b' leading to
a Fib(a,b) which will never share any term with Fib(1,2)? 
Many thanks,
É.
[I've never subscribed to Fibonacci Quarterly...]