@Carl Love 

The following code finds the same solutions as your code, but it works 17 times faster. In fact, it does not matter, because in any of these solutions, excepted one solution,  the condition, that the distinct letters represent distinct digits, does not hold.

restart;

t:=time():

[seq(seq(seq([CNRP=9*10^3+N*10^2+R*10+P, CPP=9*10^2+P*10+P, KHMER=9*10^3+N*10^2+R*10+P+9*10^2+P*10+P], N=0..9), R=0..8, 2), P=0..9)]:

L:=select(n->is(convert(rhs(n[3]),base,10)[1]=convert(rhs(n[1]),base,10)[2] and nops(convert(rhs(n[3]),base,10))=5), %):

time()-t;

nops(L);

                                   0.031 

                                     94

Different letters denote different figures.  DirectSearch  package ignores the condition  nops({C, E, H, K, M, N, P, R}) = 8

Different letters denote different figures.  DirectSearch  package ignores the condition  nops({C, E, H, K, M, N, P, R}) = 8

@Carl Love 

Of course, calculated solutions are the all solutions. I meant that the code itself can be different. 

@Carl Love 

Of course, calculated solutions are the all solutions. I meant that the code itself can be different. 

@Carl Love 

You wrote "The step length AD must be a multiple of primorial(n) where n is the progression length".  This is not true.

The example:   7, 157, 307, 457, 607, 757, 907

@Carl Love 

You wrote "The step length AD must be a multiple of primorial(n) where n is the progression length".  This is not true.

The example:   7, 157, 307, 457, 607, 757, 907

Why  AD=210 ?  What is the justification for?  It is obvious only that the difference of the progression  should be an even.

Why  AD=210 ?  What is the justification for?  It is obvious only that the difference of the progression  should be an even.

Mathematics is both a tool and an art, and that's fine.

@Markiyan Hirnyk 

Thank you!
You are right.  I did not notice that in the third quarter the plots are superimposed on one another. But Maple is also wrong, the solutions  {a=0, b=0}  and  {a=1, b=1}  are lost.

@Markiyan Hirnyk 

Thank you!
You are right.  I did not notice that in the third quarter the plots are superimposed on one another. But Maple is also wrong, the solutions  {a=0, b=0}  and  {a=1, b=1}  are lost.

@Markiyan Hirnyk

Try  RealDomain:-solve(sys, symbolic=false);

@Markiyan Hirnyk

Try  RealDomain:-solve(sys, symbolic=false);

@Markiyan Hirnyk 

Take a closer look:

sys := [sqrt(sin(x)^2+1/sin(x)^2)+sqrt(cos(y)^2+1/cos(y)^2) = sqrt(20*y/(x+y)), sqrt(sin(y)^2+1/sin(y)^2)+sqrt(cos(x)^2+1/cos(x)^2) = sqrt(20*x/(x+y))]:

A := lhs(sys[1])+lhs(sys[2]);