Excerpted from Beachy/Blair, Abstract Algebra, 2nd Ed. © 1996

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§ 9.3 Some Diophantine Equations

 
Theorem 9.3.3. Every prime in Z of the form 4k+1 can be written as the sum of two squares.

 
Theorem 9.3.8. The equation x3 + y3 = z3 has no solution in the set of positive integers.

 


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