Define a sequence of functions f₀, f₁, f₂, ......, by

f₀(x)= 8, for all real x, and
f_n+1(x) = sqrt(x² + 6f_n(x)); for all real x and all non-negative integers n.

Solve the equation

f_n(x)= 2x

(In reply to re(4): Solution? by tomarken)

It seems likely that x=4 is the only solution for any n>0.  However, finding a convincing argument for why that is true appears to require some trick that we have yet to discover.

Posted by Richard on 2006-11-19 18:02:36