Exponent of 3

33=27,2+7=934=81,8+1=9310=59049,5+9+0+4+9=27315=14348907,1+4+3+4+8+9+0+7=36\begin{array} {l l l } 3^3 = 27, & 2 + 7 &= 9 \\ 3^4 = 81, & 8 + 1 &= 9 \\ 3^{10} = 59049, & 5 + 9 + 0 + 4 + 9 &= 27 \\ 3^{15} = 14348907, & 1 + 4 + 3 + 4 + 8 + 9 + 0 + 7& = 36 \end{array}

True or False?

For any positive integer k>1k>1, the sum of digits of the representation of 3k3^k is always divisible by 9.


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