On the Equation $a^2+bc=n$ with Restricted Unknowns

Volume 64 / 2016

M. Skałba Bulletin Polish Acad. Sci. Math. 64 (2016), 137-145 MSC: 11E25, 11E16, 11A55. DOI: 10.4064/ba8079-11-2016 Published online: 14 December 2016


We extend our previous results concerning the equation $a^2+bc=n$ to all primes $n$ and deal also with the general case of non-square $n$. Moreover, we provide partial results on patterns of ‘1’ and ‘11’ in the continued fractions of $\sqrt {n}$.


  • M. SkałbaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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