MathNet 2026 — Part 09 Question 115

The tower function of twos, $T(n)$, is defined by $T(1)=2$ and $T(n+1)=2^{T(n)}$ for $n \geq 1$. Prove that $T(n)-T(n-1)$ is divisible by $n!$ for $n \geq 2$.