Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Show that the Diophantine equation $x^{4} - y^{4} = z^{2}$ has no solutions in nonzero integers using the method of infinite descent.

Thanks for any help on this proof. Infinite descent has me kind of stumped because the book does not clearly explain the concept.

share|improve this question
5  
Wikipedia article on infinite descent gives a proof of this. See also Proof of Fermat's Last Theorem for specific exponent. –  Martin Sleziak Apr 29 '12 at 7:52
    
The idea of infinite descent is that if you can prove that form a positive solution you can find a "smaller" positive solution, then this would set up a potential infinite sequence of smaller and smaller positive integer solutions. Since the positive integers don't have infinite strictly descending sequences, that means the sequence can never get started. –  Arturo Magidin Apr 29 '12 at 20:39
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.