@acer Instead of writing (2*x-3)^2 = (2*x)^2 - 2*3*(2*x) + 3^2, can I get (2*x-3)^2 = (2*x)^2 - 2*(2*x)*3 + 3^2?

@acer Thank you very much.

@acer How can I joint two commands  Display(temp, inert=false) and value(temp); to get answers like this x^2 - 2x - 3x + 6 = x^2 - 5 x + 6.

Consider f(x) = (x-a)^4  + (x-b)^4 - c;

We have

f'(x) = 4*(x - a)^3 + 4*(x - b)^3;

f''(x) = 12*(x - a)^2 + 12*(x - b)^2 >=0
This means that the graph is concave up everywhere, therefore f(x) = 0  cannot have more than two real roots.

@Carl Love 

@Carl Love I try with your c. I got

There is an answer
https://www.mapleprimes.com/questions/231668-How-To-Find-Number-A-B-C-D-M-So

@acer Thank you very much.

@acer 

How a bout this? I can not get the result?

restart;
with(PolyhedralSets):

ps := PolyhedralSets:-PolyhedralSet([[1/2,1/2,0],[-1/2,1/2,0],[-1/2,-1/2,0],[-1/4,1/4,sqrt(15)/4],[1/4,-1/4,sqrt(15)/4]],[x,y,z]):

@Kitonum Thank you very much. Can I get another list of vetors?

@mmcdara I want arithmetic progression version.

@vv Thank you very much. Now, it works.

@vv I copied your code, when I compile, I get "error, missing operation".

@Kitonum I added two conditions and igcd(a,b,c)=1 and igcd(x,y,z)=1. 

@vv Thank you very much.