Find-a-natural-number-n-such-that-3-9-3-12-3-15-3-n-is-a-perfect-cube-of-an-integer-

Question Number 19192 by Tinkutara last updated on 06/Aug/17

Find a natural number^{'} n^{'} such that

3^{9} + 3^{12} + 3^{15} + 3^{n} is a perfect cube of

an integer .

Commented by Tinkutara last updated on 07/Aug/17

Thank you very much Sir!

Commented by RasheedSindhi last updated on 07/Aug/17

3^{9} + 3^{12} + 3^{15} + 3^{n}

n = 14

3^{9} + 3^{12} + 3^{15} + 3^{14}

= 3^{9} + 3^{12} + 3^{14} + 3^{15}

= {(3^{3})}^{3} + 3 {(3^{3})}^{2} (3^{5}) + 3 (3^{3}) {(3^{5})}^{2} + {(3^{5})}^{3}

= {(3^{3} + 3^{5})}^{3}