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This analysis finds solutions of a Diophantine equation involving Fibonacci numbers in positive integers, suggesting relationships among them.
In this paper, we find all the solutions of the Diophantine equation Fk,1²+2Fk,2²+⋯ +mFk,m²=Fk,nq F k , 1 2 + 2 F k , 2 2 + ⋯ + m F k , m 2 = F k , n q in positive integer variables ( m , n ), where Fk,i F k , i is the iᵗʰ i th term of the kᵗʰ k th Fibonacci sequence, k a positive integer and q∈ \1,2\ q ∈ { 1 , 2 } .
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Tchammou et al. (2026) studied this question.
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