Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations

Most mathematics books chase a topic or a theory. This one chases a particular question from the first results, due to Fermat, all the way to a complete solution. The author does his best to keep the reader with him all along, but it’s a long road. New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Those seem straightforward enough, and suggest a conjecture that the primes that can be written as \(x ny 2 was published in 2022 by the American Mathematical Society. The main features of the third edition are: Every prime number which surpasses by one of three a multiple of eight is composed of a square and the double of another square.…

Typographical Errors in the Second Edition

Fermat managed to find complete solutions for \(n=1,2,3\). He showed that in those cases there is a congruence condition on the prime \(p\) that decides the question. For example: Every prime number which surpasses by one a multiple of four is composed of two squares. …