Fibonacci Numbers of the Form
نویسنده
چکیده
(*)' Fn = ox. In [1], Cohn solved (*) for c = 1, 2. In [9], we found all solutions of O ) such that <? is prime and either o = 3 (mod 4) or c < 10,000. Harborth & Kemnitz [4] have asked for solutions of (&) for composite values of o. Clearly, it suffices to consider only squarefree values of c. If c < 1000, then c has at most three distinct odd prime factors. Therefore c = kp where p is prime and k = 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 38, 39, 42, 51, 55, 65, 66, or 70. In this paper, we solve (*) for each of the above values of c. In the cases k = 2, 13, 26, 34, our results are valid only for p < 10,000; in the other cases, there are no restrictions on p. These results are listed in Table 1. Combining these new results with those from [1] and [9], we obtain all solutions of (*) such that 1 < a < 1000. We list these solutions in Table 2.
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