67 research outputs found
On a class of Lebesgue-Ramanujan-Nagell equations
We deeply investigate the Diophantine equation in
integers and , where and are given
coprime positive integers such that . We first solve
this equation for prime , under the condition , where
denotes the class number of the quadratic field
. We then completely solve this equation for both
and primes under the assumption that . We also
completely solve this equation for and , under the
condition . For some fixed values of and , we derive
some results concerning the solvability of this equation.Comment: 13 Pages. A minor correction in Theorem 1.2 has been made. Comments
are most welcome
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