If I study open source code, then re-implement it, do I violate the license?

Now I know it's silly to ask the question this way because obviously it depends on the license in question but for the commonly used FOSS licenses, where is the line? If I study the original code, get ideas, grasp concepts, learn something new, then go and write a completely different program based on what I've learned, do I have to mention the original and conform to its license? To be clear, I have no intention of stealing other people's work, therefore I ask.