169. An Impressive Diophantine Equation. Find at least one solution to the equation $a^{3}+b^{4}=c^{5}$ in positive integers.
169. Since $2^{24}+2^{24}=2^{25}$, we get $\left(2^{8}\right)^{3}+\left(2^{6}\right)^{4}=$ $\left(2^{5}\right)^{5} ;$ from which $a=256, b=64, c=32$.

[Leo Moser, M. M., 26, 53 (September 1954).]