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Divergent sum of inverses

Source: Miklós Schweitzer 2014, P5

December 22, 2014
superior algebrasuperior algebra unsolved

Problem Statement

Let α \alpha be a non-real algebraic integer of degree two, and let P \mathbb{P} be the set of irreducible elements of the ring \mathbb{Z}[ \alpha ] . Prove that ∑p∈P1∣p∣2=∞ \sum_{p\in \mathbb{P}}^{{}}\frac{1}{|p|^{2}}=\infty
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