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Consider the following scenario.

I am researching on a problem in a domain and I don't know anything about the existence of Pythagoras theorem.

After so much time of my research I figured myself that if a fact like:

the square of a side which is opposite to the 90 degrees in a triangle is equal to the sum of squares of remaining sides

exists, then my research completes and I can publish a good paper. But I never encountered Pythagoras theorem during my search of literature.

If I came to know about its existence during a discussion with a colleague or any random person, then is there any ethical need to keep him as a co-author since I struggled a lot of time and didn't find by myself?

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    In your example, you already pinned down the exact fact that you needed to complete your paper; so the other person didn't have much of a contribution except for giving you a pointer for that fact. In reality, such situations can be more messy: the other person may map your required fact to the vocabulary of another domain, or they may help you pin down the required fact in the first place. These would be more substantial contributions. – lighthouse keeper May 22 '20 at 10:52
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The International Council of Medical Journal Editors (ICMJE) has established four criteria for being considered an author. The person's contribution should fulfill all four criteria. If not, they need to be considered as a non-author contributor and their contribution acknowledged, such as in Acknowledgements section. You can read about the different criteria and designation here. To directly answer your question, the person would be a non-author contributor.

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    But surely only if the paper is published in a medical journal... – astronat May 22 '20 at 10:46
  • @astronat, I think the opinion expressed in the linked article is pretty widely shared, independent of field, though not universal. And where it is not held, there is controversy about it. Hence we get a lot of questions here from unsatisfied grad students. – Buffy May 22 '20 at 11:23
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    I am not sure how this is a full answer. The first criterion on that list is that the contribution has to be "substantial". As soon as this is the case, offering to work on the manuscript together and thus fulfilling the other three criteria is just professional courtesy. The heart of the question, which is still open, is if providing basic knowledge counts as substantial. (I think the consensus for this is a resounding no, but talking about it should be part of an answer.) – mlk May 22 '20 at 11:48

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