科研之友
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摘要
We show that if k >= 2 is an integer and (F-n((k)))(n >= 0) is the sequence of k-generalized Fibonacci numbers, then there are only finitely many triples of positive integers 1 < a < b < c such that ab + 1, ac + 1, bc + 1 are all members of {F-n((k)): n >= 0}. This generalizes a previous result where the statement for k = 3 was proved. The result is ineffective since it is based on Schmidt's subspace theorem.
- 出版日期2018-7
