On the closed geodesics problem

Let $\text{bk}$ be a field of characteristic $p\ge 0$ and $X$ a simply connected finite CW complex. In this text, we prove that: {\sl if the cohomology algebra $H^{\ast }(X;\text{bk})$ is generated, as an algebra, by at least two linearly independent elements, then the sequence of Betti numbers ${(\dim H^n(LX;\text{bk}))}_{n\ge 1}$ grows unbounded.} This provides a complete solution of the closed geodesics problem.