engleski

D(4)-pairs {; ; F_{; ; 2k}; ; , F_{; ; 2k+6}; ; }; ; and {; ; P_{; ; 2k}; ; , P_{; ; 2k+4}; ; }; ;

We call the set of m positive distinct integers a D(4)-m-tuple if the product of any of its two elements increased by 4 is a perfect square. Let k≥1 be an integer and let F_k be the k-th Fibonacci number and P_k k-th Pell number. In this paper we prove that the pairs {; ; F_{; ; 2k}; ; , F_{; ; 2k+6}; ; }; ; and {; ; P_{; ; 2k}; ; , P_{; ; 2k+4}; ; }; ; cannot be extended to a D(4)-quintuple.

Diophantine m-tuples

nije evidentirano