A Pellian equation with primes and applications to D(-1)-quadruples

Andrej Dujella, Mirela Jukić Bokun, Ivan Soldo

In this paper, we prove that the equation $x^2-(p^{2k+2}+1)y^2=-p^{2l+1}$, $l\in \{0,1,\dots ,k\},k\ge 0$, where $p$ is an odd prime number, is not solvable in positive integers…