For any positive integers $k$ and $l$, does the equation $$\left(\sum_{i=1}^k \frac{1}{p_i}\right) \left(\sum_{j=1}^l \frac{1}{q_j}\right) = 1$$ have solutions in distinct primes, that is, $p_1, p_2, \dots, p_k, q_1, q_2, \dots, q_l$ are distinct?
2026-02-22 23:40:36.1771803636
Product of sum of reciprocals
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