engleski

On the D(4)-triple {;F_{;2k};, F_{;2k+6};, 4F_{;2k+4};};

Let k be a positive integer. In this paper, we study the D(4)-quadruples {; ; F_{; ; 2k}; ; , F_{; ; 2k+6}; ; , 4F_{; ; 2k+4}; ; , d}; ; , where F_k is a kth Fibonacci number. We prove that if d is a positive integer such that the product of any two distinct elements of the set increased by 4 is a perfect square, then d = 4F_{; ; 2k+2}; ; F_{; ; 2k+3}; ; F_{; ; 2k+5}; ; . Therefore, we prove the uniqueness of the extension of another D(4)-triple involving Fibonacci numbers.

Diophantine m-tuples; Pell equations; Fibonacci numbers; Baker's method

nije evidentirano