A special case of Fermat’s conjecture
Part of the Universitext book series (UTX)
Algebraic number theory is essentially the study of number fields, which are the finite extensions of the field ℚ, of rational numbers. Such fields can be useful in solving problems which at first appear to involve only rational numbers. Consider, for example, this problem:
Find all primitive Pythagorean triples: i.e., integer solutions of x2 + y2 = z2 having no common factor.
KeywordsPrime Ideal Number Field Unique Factorization Principal Ideal Ideal Class
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© Springer-Verlag, New York Inc. 1977