I did two polar plots as you see and wanted to color the region between them.

> with(plots);
> a1 := polarplot(1, t = 0 .. 6*Pi*(1/3), thickness = 2, filled = true, color = black);
> a2 := polarplot(2*cos(t), t = 0 .. 6*Pi*(1/3), thickness = 2);
> a3 := polarplot(2*cos(t), t = -(1/3)*Pi .. (1/3)*Pi, filled = true, thickness = 2);
> display(a1, a2, a3);

The program makes the region colored red but there is an overlapping part which...

Recently, I encountered the problem in which one's asked to investigate if the following fraction is an integer or not. Of course the problem has an theoritical approach, but I wanted to make the problem dynamic. The fraction is p=(k^2-87)/(3k+117) and we want to find k in which p is an integer. What I did is to use the function msolve and a loop for but it gives my just the empty set which is incorrect. Any hint? Thanks

Before I brought up my question here, I had asked it [here](http://stackoverflow.com/q/16852062/1842737). Thanks for your hint and the time.

Dear Friends, I asked my question here http://stackoverflow.com/questions/13677399/why-this-program-cant-work and got one answer. I don't want to prove that if Maple is unable solve my problem or not, but want to know if you agree with the answer there. What can I do with this problem noted there which happened during teaching in the class and made me ashamed badly.

Best and Thanks.

Assume; we have a set of elements like A:={2, 3, 6,24,7,5,25,100,124,32,...} with #A=20 and moreover, we know that some of these elements satisfy an equation, for example a^k=b^2 for some positive integers k ( a  and b are in A).

For example if a=2 be in A and b=64 be also in A, then k=6. I have written some loops including for and if, but I have exhausted. I see, I can’t arrange and link these functions together properly.