MathDB

N5

Part of 2007 Balkan MO Shortlist

Problems(1)

sum of q_ibeta_i is greater than p^2

Source: Balkan MO ShortList 2007 N5

4/6/2020
Let p≥5p \geq 5 be a prime and let \begin{align*} (p-1)^p +1 = \prod _{i=1}^n q_i^{\beta_i} \end{align*} where qiq_i are primes. Prove, \begin{align*} \sum_{i=1}^n q_i \beta_i >p^2 \end{align*}
prime numbersInequalitynumber theory