On the Diophantine equation (( c + 1) m 2 + 1) x + ( cm 2

Suppose that c m and aare positive integers with a \equiv 11,\,13 \pmod{24} In this work, we prove that when 2c+1=a^{2} the Diophantine equation in the title has only solution (x, y, z)=(1,1,2)where m \equiv \pm 1 \pmod{a}and m>a^2in positive integers. The main tools of the proofs are elementary methods and Baker's...