Elliptic Paraboloids and Gaussian Integers

This book aims in determining Gaussian integer solutions to special three dimensional surfaces namely, elliptic paraboloids represented by their corresponding ternary quadratic polynomial equations. In each illustration, different sets of Gaussian integer solutions are exhibited. It is hoped that these problems may create interest in the hearts of researchers who approach it with pure love for its own beauty. The aim here is to introduce and inspire the researchers which will end up really loving mathematics. There is no doubt that, to have a deep and thorough knowledge of the illustrations presented here, one must do a lot more than reading these problems. Always remember that "Problems are not stop signs, they are guidelines" as quoted by Robert H. Scheulter. A reasonable number of illustrations for obtaining Gaussian integer solutions to different choices of elliptic paraboloids are presented in this book. The authors believe that, on seeing the beauty of solving the special three dimensional surface in Gaussian integers, young mathematicians and researchers realize that there are other problems in the theory of Diophantine equations which are challenging in the future.