TITLE: Is it a reasonable way to write a research article assuming truth of a conjecture?
QUESTION [18 upvotes]: I have found a conjecture in a research article (published in a good journal) on number theory, which is not well known but very reasonable. Let me be clear that, there is no counter-example that vote down the conjecture, rather, its trueness has been proved in some special situation so far. I need this conjecture to develop a tool in order to write a research article. Unfortunately, I am unable to prove the conjecture as of now. Maybe others can prove it after some time.
My question:
Is it a reasonable way to write a research article assuming truth of the conjecture?

REPLY [2 votes]: This is not fundamentally different from the (fairly subtle) question of whether any mathematical result in general is "interesting". Publication typically requires (at least) a result that is both true and interesting. From a logical viewpoint, there is absolutely no problem with proving the truth of a theorem that includes a conjecture in its hypothesis. It is a theorem like any other.
Meanwhile, a major factor in what makes a result uninteresting for publication is if it can be trivially derived from simpler results. This is not an objective characteristic but a time-dependent fact of human knowledge.
In your situation, if and when the conjecture is resolved, we know it will be possible to derive your theorem trivially from a simpler result. Namely, if the conjecture is true, there will be a simpler theorem that omits the conjecture from the hypothesis, from which your theorem will follow trivially. And if the conjecture is false, your theorem will be derivable as a tautology. But I would argue that until we know which obtains, your theorem is not yet uninteresting.