find all ordered pairs of natural numbers (x,y,z) that satisfies $x^{x^y} \cdot y^{y^z} \cdot z^{z^x} = 1990^{1990} \cdot xyz (x\lt y \lt z)$
My approach was $$x^{3(x^x-1)} \lt x^{x^y-1} \cdot y^{y^z-1} \cdot z^{z^x-1} = 1990^{1990}$$ and if x is 5 -> $5^{3(5^5-1)}=5^{9372} \gt 1990^{1990}$
so $x\in \{1,2,3,4\}$,and I tried to check in cases when x=1, x=2,x=3,x=4 but I couldn't proceed.