Couple observations: Note $x,y$ odd otherwise it fails since $2\mid{1994}, 4\nmid{1994}$ Hence to bound its enough to find the largest $n$ such that $3^{n}+1<1994$ so $n<6$ Rest is pretty easy casework since $7^4=2401$ we are dealing with just $1,3,5$ and by inspection none of these work for $n=4,5,6$ For $n=3$ Check $11,9$ and neither work For $n=2$ we can manually check too lazy but prob one here

Medjl wrote: Determine all integer solutions of the equation $x^n+y^n=1994$ where $n\geq 2$ It was here. Please use the search function.