**(1) Radan Miryanov, (2) Katya Chalakova**

*(1) University of Economics – Varna (Bulgaria)*

*(2) Mathematics High School “Ivan Vazov” – Dimitrovgrad (Bulgaria)*

**Abstract.** In the present research paper a particular type of problems is examined, with an infinite number of cube roots involved. Different problems and questions are proposed and in terms of solving some examples two theorems are defined and proved.

The study could be a good base for generating various problems from this type, used in mathematical competitions, Olympiads and for preparing such events.

*Keywords:* infinite number; cube roots; math competitions

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