The paper proves a five-term linear independence theorem for certain Lambert series, implying the Fibonacci and Lucas reciprocal sums over prime squares are linearly independent with 1 over Q(√5).
Bundschuh, Arithmetical investigations of particular Wynn power seri es
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Linear independence results for certain sums of reciprocals of Fibonacci and Lucas numbers
The paper proves a five-term linear independence theorem for certain Lambert series, implying the Fibonacci and Lucas reciprocal sums over prime squares are linearly independent with 1 over Q(√5).