Re: what are the conditions on f ?

hagman wrote :

On 27 Jan., 23:17, tommy1729 <tommy1...@xxxxxxxxx>
wrote:
hagman wrote :



On 27 Jan., 22:42, hagman <goo...@xxxxxxxxxxxxx>
wrote:
On 27 Jan., 00:15, 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

If f is injective, g[1,t]arbitrary, and g[2,t]
:=
f(g[1,t])
then the equation holds for
b_2 = b = arbitrary, c=arbitrary, a=1, a_2=2.

Oops, "f injective" is of course not necessary.
When I started replying, I was heading for some
other
conditions.

what you say is true hagman...

but not of much help.

I take the freedom to blame that on you not being
specific enough
in your problem description. ;)

dont be so ullrich ;-)



Jack and Jim got lost in a foggy cloud while hot air
balloning.
After an hour or so they get out of the cloud and see
a man
walking on the gruond.
They ask him: "Hey, hello, good man! Can you please
tell
us where we are?"
The man ponders for a minute or two and then replies:
"Yes, I can - you are in a basket under a hot air
balloon"
Jack and Jim look at each other, totally puzzled.
Then Jack realizes: "This must be a mathematician!" -
"Why?" -
"1. The answer is absolutely correct
2. It is of no use whatsoever
3. It took him long to find out something we already
y knew"


dont be so galathaea. :)



perhaps you want to look at the reply i gave to
gerry here , it might give you a better idea of what
i want.

Yes, it shows me that you are interested in the case
where f and g
are algebraic or transcendental functions.

rather transcendental ; the algebraic is just an example for clarification.


But I guess you should rather be more specific about
what kind of infinitely many integer tuples you are
interested in.

just the ones i gave mapping from (a,b,c) to (a_2,b_2c)

the reason is simplicity.





thanks for the effort though.

once again thanks for the effort.



regards
tommy1729


regards
tommy1729
.

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