You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
You cannot.
No, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
Counterexamples are used to test the validity of conjectures by providing a specific instance where a conjecture fails. If a counterexample is found, it refutes the conjecture, demonstrating that it is invalid. Conversely, if no counterexamples can be found despite thorough testing, it supports the conjecture's validity, although this does not prove it universally true. Thus, while counterexamples are critical for refutation, their absence strengthens the case for a conjecture, though further proof may still be needed for confirmation.
z5 is an expression, not an equation and so cannot have roots.
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, a theorem cannot have a counterexample, as a theorem is a statement that has been proven to be true under a specific set of conditions. A counterexample, on the other hand, demonstrates that a statement or conjecture is false by providing an instance where the statement does not hold. If a counterexample exists, the statement is not a theorem.
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.