Let's start with some common sense.
17 has to be the sum of two powers
The only "powers" ≤ 17 are 1, 4, 8, 9, and 16
well, 8 + 9 = 17
2^3 + 3^2 = 17, and sure enough 2+3 = 5
so x = 2, y = 3, or
x = 3, y = 2 are solutions
the graph of x^y + y^x = 17 looks like this with the help of Wolfram
https://www.wolframalpha.com/input/?i=graph+x%5Ey+%2B+y%5Ex+%3D+17+
and x + y = 5 is a straight line, it looks like these are the only two solutions.
Solve x^y+y^x=17
X+y=5
2 answers
yes
1 answer