On the Diophantine equations z<sup>2</sup> = k(k<sup>2</sup> + 3) and z<sup>2</sup> = k(k<sup>2</sup> + 12)
Keywords:Diophantine equation, analytic solution, GP/PARI
This paper provides an analytical method of finding all the (positive, integral) solutions of the Diophantine equation z2 = k(k2+3). We also prove analytically that the Diophantine equation z2 = k(k2+12) has no positive, integer solution.
J. Bangladesh Acad. Sci. 45(1); 127-129: June 2021