According to this question :-Why is so important if a question is homework? it is not right if you don't show any work in solving or answering you own question and shows academic dishonesty but if the question is more complicated and you cant solve it by using normal means. By meaning "not solvable using normal means" I mean that question is out of the OP's reach and he/she has found it from his/her daily mathematics. Will the same claim be made and would the question still show academic dishonesty?
A general request made towards askers is to provide context and what this can mean is detailed for example in this meta-answer; it is not only or even mainly about "show your work."
This also applies to conjectures the user came up with, I would even say it is especially important in this case.
It can make a significant difference for how to approach a questions whether:
The question is a conjecture of the asker.
The question is a conjecture the asker read somewhere (where exactly?).
The question is an exercise form a textbook or a contest-problem (which book?).
Thus, one should at least state that the problem one presents is a conjecture one came up with.
Then, one might continue to explain what made one conjecture this fact in the first place, for example it could be: numerical evidence (some details?), or analogy with another problem (which problem?), or heuristics suggest it is true, and so on. If one did already try to solve it in some way one could share this information, too.
Yet again, as a minimum one should say it is a conjecture one came up with.