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Challenge: Can you find all the integers $a$, $b$, $c$ satisfying $2a^ + 3b^ = 5c^$? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of $a$, $b$, $c$ will usually be large. So the challenge remains ... Find all integers$a$, $b$, $c$satisfying$2a^ + 3b^ = 5c^$.

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 collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.