@article{Journal-Maths-Stats, author = {Sudhanshu Aggarwal}, title = { Solution of the Diophantine Equation 323x + 85y = z2}, journal = {Journal of Advanced Research in Applied Mathematics and Statistics}, volume = {8}, number = {1&2}, year = {2023}, keywords = {}, abstract = {Diophantine equations have numerous applications in Algebra, Chemistry, Astrology, Cryptography and Trigonometry. In this paper, author examined the Diophantine equation 323x + 85 =z2, where x, y, z are non-negative integers, for its non-negative integer solutions. For this, author used Catalan’s conjecture and proved that (x, y, z) = (1, 0, 18) is the unique non-negative integer solution of the Diophantine equation 323x + 85 =z2, where x, y, z are non-negative integers.}, issn = {2455-7021}, pages = {6--9}, url = {http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/731} }