On x<sup>n</sup> + y<sup>n</sup> = n!z<sup>n</sup>
On x<sup>n</sup> + y<sup>n</sup> = n!z<sup>n</sup>
Abstract 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 ∈ N + and n > 2. But, contrary …