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Question: Two Diophantine equations

Question:Two Diophantine equations

Alfred_F 305 Maple
programming numerical-analysis diophantine_equation
May 16 2025
1

I recently solved the following Diophantine equations:
tan(3*pi/x)+4*sin(2*pi/x)-sqrt(x)=0
and
tan(13*pi/x)+4*sin(19*pi/x)-sqrt(x)=0
Unlike my old "pencil and paper" solution, I used Maple to practice with some sub-calculations to get some guesses for the solution. To confirm my guesses, I inserted them into the equations and used "simplify." The result was "zero." Is this "zero" the mathematically exact zero, or does Maple display a very small real number as "zero" after applying "simplify"?
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