The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial p...The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial properties of the m-tuplings Morse sequence, we mainly obtain this sequenee is an admissible sequence and the other two sequenees generated by it are also admissible sequences, which extends the conclusion that the Thue-Morse sequence is an admissible sequences.展开更多
A set[ai,a2,...,am)of positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all 1≤i<j≤m.Let(a,b,c)be the Diophantine triple with c>max(a,b].In this paper,we find the condition for...A set[ai,a2,...,am)of positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all 1≤i<j≤m.Let(a,b,c)be the Diophantine triple with c>max(a,b].In this paper,we find the condition for the reduction of third element c,and using this result,we prove the extendibility of Diophantine pair[F_(k)-1F_(k+1),F_(k-2)F_(k+2)],where Fn is the n-th Fibonacci number.展开更多
基金Supported by the Special Funds for Major StateBasic Research Projects (60472041)
文摘The m-tuplings Morse sequence, as a fixed point of a constant length substitution, was discussed. An equivalent definition was given by the property of the m-adie development of the integers. Using the combinatorial properties of the m-tuplings Morse sequence, we mainly obtain this sequenee is an admissible sequence and the other two sequenees generated by it are also admissible sequences, which extends the conclusion that the Thue-Morse sequence is an admissible sequences.
基金supported by the National Research Foundation of Korea(NRF)gi funded by the Korea government(MSIT)(No.2019R1G1A1006396).
文摘A set[ai,a2,...,am)of positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all 1≤i<j≤m.Let(a,b,c)be the Diophantine triple with c>max(a,b].In this paper,we find the condition for the reduction of third element c,and using this result,we prove the extendibility of Diophantine pair[F_(k)-1F_(k+1),F_(k-2)F_(k+2)],where Fn is the n-th Fibonacci number.
