# Find us out, you detectives!

Number Theory Level pending

Let $$S_{k}$$ denote the sum of digits of a number. Then, what are the two numbers m and n such that,

$$S_{k}(m^{1})$$ = $$n^{1}$$

$$S_{k}(m^{2})$$ = $$n^{2}$$

$$S_{k}(m^{3})$$ = $$n^{3}$$

$$S_{k}(m^{4})$$ = $$n^{4}$$

What is the sum of these two numbers?

Note that m,n>1

×