sum of q_ibeta_i is greater than p^2
Source: Balkan MO ShortList 2007 N5
April 6, 2020
prime numbersInequalitynumber theory
Problem Statement
Let be a prime and let
\begin{align*} (p-1)^p +1 = \prod _{i=1}^n q_i^{\beta_i} \end{align*}
where are primes. Prove,
\begin{align*} \sum_{i=1}^n q_i \beta_i >p^2 \end{align*}