Furdui–Sîntămărian's consecutive harmonic-number product conjecture
Let q≥1q\geq 1q≥1 be an integer, and let Hk=∑j=1k1jH_k=\sum_{j=1}^k\frac{1}{j}Hk=∑j=1kj1 denote the kkkth harmonic number. For rational numbers αq,2,αq,3,…,αq,q+2\alpha_{q,2},\alpha_{q,3},\ldots,\alpha_{q,q+2}αq,2,αq,3,…,αq,q+2, conside…