Applications of Bertrand's postulate and its extensions in math olympiad-style problems
Prime numbers are one of the fundamental entities in Number Theory. The guarantee of the existence of a prime number within a certain interval can be helpful in solving several types of problems. The Bertrand-Chebyshev theorem, also known as Bertrand’s postulate, can be very useful in this context. Here we present several solved examples where it can be successfully used. A particular emphasis is placed on Math olympiad-style problems and therefore the article is based solely on elementary techniques. In addition to solved examples, this work also contains a brief historical and theoretical background, a list of some stronger results as well as a set of problems for self-study.