Re: what are the conditions on f ?

On Jan 27, 12:15 am, tommy1729 <tommy1...@xxxxxxxxx>
wrote:
what are the conditions on f and g ?

for an infinite amount of
non-zero integers a , b , a_2, b_2 and c.

f(g[a ; b*f(c)]) = g[a_2 ; b_2*f(c)]

e.g. : f = sqrt and g = sum are possible solutions.

regards
tommy1729

Hi Tommy,

can you give an example?

Gerry

yes , actually , i did => f = sqrt and g = sum

wich then gives equations like

sqrt( 3 + 2*sqrt(2) ) = 1 + sqrt(2).

sqrt( 49 + 12*sqrt(5) ) = 2 + 3*sqrt(5).

in general when g and f are algebraic functions as above , its quite simple and reduces to basic algebraic ring theory, elementary galois theory and diophantine equations.

most intresting is : what are the conditions on f and g , especially if f and g are transcendental functions.

is this to be called transcendental ring theory , transcendental galois theory , ... im not sure.

regards
tommy1729
.