SORRY, I apologize very much I made a confusion between z1*z2 and z1+z2

This true that( z1^2+z2^2+2*z1*z2)/(z1+z2)=z2/z1+z1/z2+2 how to obtain this egality ? Thank you.

How to show directly that is((z1+z2)^2/(z1+z2)=z2/z1+z1/z2+2) is true ? Thank you.

How to find n triples with such a procedure :
Tri:=proc(Y,n)#Y a triple
local m:
global &*:#coming from previus calculations
m:=Y&*(Y&*(Y&*Y))):#n times
RETURN(m)
end:Thank you for your help.

I have an error for the third line : error, invalid input: f expects its 1st argument, T, to be of type And(list...) but received p.

How to correct. Thank you.

Thank you. An other question : represent module points between 1 and 2 and argument points Pi/4 ?

Sorry for my errors.
I tried to adapt the program to cubes 
 

Cubes := `~`[`^`]([`$`(1 .. 10)], 3); Cubes := [1, 8, 27, 64, 125, 216, 343, 512, 729, 1000] for n from 100 to 100+13^(3) do found:=false ; for m to nops(Cubes) do for c in combinat:-choose(Cubes,m) do if add(c)=n then printf(cat("\n%d = %d^3", " + %d^3"$(m-1)),n,root~(3,c)[]); found:=true fi until found until found; if not found then printf("\n%d: no solution",n) fi od: But it doesn't work.

restart; Squares := `~`[`^`]([`$`(1 .. 12)], 2); Squares := [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144] for n from 129 to 129+13^(2) do found=false ; for m to nops(Squares) do for c in combinat:-choose(Squares,m) do if add(x,x=c)=n then printf(cat("\\n%d = %d^2", " + %d^2"$(m-1)),n,sqrt~(c)[]); found=true fi until found until found; if not found then printf("\\n%d: no solution",n) fi od: How to avoid this message ? Error cannot determinate if this expression is true or false : found. Thank you.

In spice of this changing, there is : Error, cannot determine if the expressionis true or false : found

still an error ! Thank you

I have this error with this last program; How to correct it ? Thank you.

For a more concise response could use fprint ? Thank you.

How to present the results, one number per line ? Thank you

How to find out the equation of the curve from t and t1 ? (that i found by hand calculation :
y*y^2*(2*x+p)*(2*x+p1)+(4*x^2-p*p1)^2=0); Thank you.
 

with debug(BISSEC);
I am getting : Error in BISSEC (now at the top level)=invalid left hand side in assignment. What can I do ? Thank you.