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On xn + yn = n!zn

On xn + yn = n!zn AbstractIn p. 219 of R.K. Guy's Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation xn + yn = n!zn has no integer solutions with n ∈ N+ and n > 2. But, contrary to this expectation, we show that for n = 3, this equation has in finitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd(x, y, z) = 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

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Publisher
de Gruyter
Copyright
© 2018 Susil Kumar Jena, published by Sciendo
ISSN
2336-1298
eISSN
2336-1298
DOI
10.2478/cm-2018-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractIn p. 219 of R.K. Guy's Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation xn + yn = n!zn has no integer solutions with n ∈ N+ and n > 2. But, contrary to this expectation, we show that for n = 3, this equation has in finitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd(x, y, z) = 1.

Journal

Communications in Mathematicsde Gruyter

Published: Jun 1, 2018

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