You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
You cannot.
z5 is an expression, not an equation and so cannot have roots.
Yes, postulates are accepted without proof and do not have counterexamples.
True but do your math! we all know your using Odyssey ware lol
Counterexamples in Topology was created in 1978.
Counterexamples in Topology has 244 pages.
You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
Sometimes Yes, as in Pythagoras' Theorem. Other times No, for as Godel's Incompleteness Theorem shows, there will be complete bodies of knowledge in which there will be truths that cannot be proven, and falsities which cannot be denied. [I paraphrase his theorem.]
A theorem is a proved rule but an axiom cannot be proven but is stated to be true.
You cannot.
No. There are many counterexamples including trapezoids and kites.
One is enough.
cannot be determined
Because, this theorem comes from the law of sines which is completely a triangle law and the law of sines can not be applied on other polygons.
Cannot be determined.
The triangle concerned MUST be a right-angle triangle. If one of the angles is not 90 degrees, you cannot use the Pythagorean theorem! Also, it must be remembered that the theorem only involves the magnitudes (lengths of the sides), you can't use it on i-j-k vectors or the like, only their magnitudes. As a result, it cannot tell us anything about the directions or angles between lines. Other than that, the Pythagorean theorem is incredibly sound!