This analysis uncovers nonnegative solutions for a diophantine equation involving Fibonacci numbers, suggesting connections to number theory.
Let ???????? be the ????-th Fibonacci number. In this paper, we show that the only nonnegative solutions (????, ????, ????) of the Diophantine equation ???? 2 ???? + ???? 2 ???? = 2 ???? with ???? ≥ ???? ≥ 0 are (1, 0, 0), (2, 0, 0), (3, 0, 2), (6, 0, 6), (1, 1, 1), (2, 1, 1), (2, 2, 1), (3, 3, 3), (6, 6, 7)
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Jeong et al. (2025) studied this question.
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