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On x n + y n = n ! z n

Susil Kumar Jena (2018)

Communications in Mathematics

In 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 x n + y n = n ! z n has no integer solutions with n + and n > 2 . But, contrary to this expectation, we show that for n = 3 , this equation has infinitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd ( x , y , z ) = 1 .

One Erdös style inequality

Tomáš J. Kepka, Petr C. Němec (2019)

Commentationes Mathematicae Universitatis Carolinae

One unusual inequality is examined.

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