The answers given are indeed correct in that they give the correct usage for a plural:
There is no problem. (singular)
There are no problems. (plural)
However, it is important to note that when one says "There is no problem", the sentence already negates multiple problems. By saying there is no problem, we mean that there is not even one single problem - not one - not any - none at all.
Therefore, the plural "There are no problems" is redundant; even if there were multiple problems and now they have all been cleared up, the singular 'no problem' still covers this.
Hope that helps.