engleski

The extension of the D(−k)-triple {;1, k, k + 1}; to a quadruple

Let k be a positive integer. In [3], it is conjectured that if {; ; ; k, k + 1, c, d}; ; ; is a D(−k)- quadruple with c < d, then c=1 and d=4k+1, in which case 3k+1 must be a square. In this paper, we confirm the above conjecture for k of the form k=l^2−1, where l is a positive integer such that l≥3.

Diophantine m-tuples ; Pellian equations ; hypergeometric method ; linear forms in logarithms of algebraic numbers

nije evidentirano