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Description of  A Gateway to Number Theory: Applying the Power of Algebraic Curves

A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables $a$, $b$, $c$ into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to $2a^{2} + 3b^{2} = 5c^{2}$ is included in the book.) In addition to equations of degree two, the book addresses degree-three equations–a branch of number theory that is today something of a cottage industry, and these problems translate into ""elliptic curves''. This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp.