Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) - ISBN:0387902309

Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics)

Date: 14 April 2011, 10:40

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Since it is likely that many people will open this book wanting to know what the current state of knowledge about Fermat's Last Theorem is, and since the book itself will not answer this question, perhaps the preface should contain a few indications on the subject. Fermat's Last Theorem is of course the assertion (not a theorem) that the equation xn+y" = z" has no solution in positive whole numbers when n>2. It is elementary (see Section 1.5) to prove that x4+y4 = z4 is impossible. Therefore the original equation is impossible whenever n is divisible by 4. (If n = 4k then xn+yn = zn would imply the impossible equation X4+ Y4-Z4 where X = x\ Y=y\ and Z-z*.)

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