A Gateway to Number Theory - Applying the Power of Algebraic Curves

Challenge: Can you find all the integers $a$, $b$, $c$ satisfying $2a^{2} + 3b^{2} = 5c^{2}$? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! A major advance in number theory means this book can give an easy answer to this and countless similar questions.