This  is a question from https://mathematica.stackexchange.com/questions/239055/how-to-reduce-the-time-to-solve-this-system-of-equations. How to reduce the time in Maple?
 

  {x, y, z, a, b, m, n} /. Solve[{1/x + 1/y == 1/z, a/x  + b/y == m/n, 2 <= x <= 30, 2 <= y <= 30, 1 <= z <= 30, 2 <= a <= 10, 2 <= b <= 10, a > b, 2 <= m <= 10, 2 <= n <= 10, x > y, GCD[m, n] == 1, GCD[a, b, m] == 1, m <= n}, {x, y, z, a, b, m, n}, Integers]

I am trying to find one option so that  a sphere is tangent with every edge of a tetrahedron. Suppose tetrahedron OABC, here O(0,0,0), A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3).  How to find a sphere is tangent with every edge of a tetrahedron?

I am trying to  find the funtion of this graph 

I tried
f := x -> a12*x^12 + a1*x^11 + a2*x^10 + a3*x^9 + a4*x^8 + a5*x^7 + a6*x^6 + a7*x^5 + a8*x^4 + a9*x^3 + a10*x^2 + a11*x + a13;
solve([f(-4) = 3, f(-3) = 1, f(-2) = 1, f(-1) = 1, f(0) = 0, f(1) = -1, f(3) = -5, f(4) = -5, f(5) = 1, eval(diff(f(x), x), x = -2.5) = 0, eval(diff(f(x), x), x = -1.5) = 0, eval(diff(f(x), x), x = 3.5) = 0, f(6) = 3], [a12, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a13]);
I got

[[a12 = 4.697405911*10^(-6), a1 = -0.00006250181861, a2 = -1.444112429*10^(-6), a3 = 0.002660698702, a4 = -0.004689494622, a5 = -0.04291772722, a6 = 0.08407481146, a7 = 0.3251529098, a8 = -0.4752692626, a9 = -1.066462933, a10 = 0.3958806924, a11 = -0.2183704462, a13 = 0.]]

plot(4.697405911*10^(-6)*x^12 - 0.00006250181861*x^11 - 1.444112429*10^(-6)*x^10 + 0.002660698702*x^9 - 0.004689494622*x^8 - 0.04291772722*x^7 + 0.08407481146*x^6 + 0.3251529098*x^5 - 0.4752692626*x^4 - 1.066462933*x^3 + 0.3958806924*x^2 - 0.2183704462*x, x = -4 .. 5)

It doesn't like the graph of the first picture. 

I want to find the numbers a, b, c, d, t, m, n of this equation. I tried
 

restart:
 k := 0:
 for a to 10 do
for b to 10 do 
for c to 10 do 
for d to 10 do 
for t to 2 do 
for m to 10 do
for n to 10 do 
if a > c and igcd(a, b, c, d, t, m, n) = 1 and abs(b)+abs(d)-n <> 0 then X := [solve(abs(a*x+b)+abs(c*x+d)-t*x^2+m*x-n = 0)]; if nops(X) = 6 and type(X[1], integer) and type(X[2], integer) and type(X[3], integer) and type(X[4], integer) and type(X[5], integer) and type(X[6], integer) then k := k+1; L[k] := [a, b, c, d, t, m, n, X[]] 
end if end if
end do end do end do end do end do end do end do; 
L := convert(L, list); 
k; 
L;

I can not get the result for along time. How can I get the result and reduce the time?

I am trying to find six integer numbers a, b, c, d, n, p so that this equation
abs(a*x+b)+abs(c*x+d)+x^2+n*x+p = 0
has 6 integer solutions are 1, 2, 3, 4, 5, 6. I tried
f:=x-> abs(a*x+b)+abs(c*x+d)+x^2+n*x+p;
solve([f(1) = 0, f(2) = 0, f(3) = 0, f(4) = 0, f(5) = 0, f(6) = 0], [a, b, c, d, n, p])

This equation has no solution. Is there six integer numbers a, b, c, d, n, p so that this equation has 6 integer solutions?

I have just found one solution is
solve(abs(-2*x+5)+abs(-2*x+9)-x^2+7*x-16 = 0, x);

With Mathematica, I see at here 
https://mathematica.stackexchange.com/questions/212808/find-integers-a-b-c-d-m-n-p-so-equation-has-six-distinct-solutions