0
$\begingroup$

Show that any positive integer N can be written as: $N=3^a+2^b*3^c$ or $N=2^b*3^c$, I initially thought it for N = any multiple of 3, but by dividing by 3 it should work for any N

$\endgroup$
  • 1
    $\begingroup$ Have you tried induction on $N$? $\endgroup$ – Luke Collins Oct 12 '19 at 20:57
  • $\begingroup$ How can you show it for any multiple of $3$? for example, how can you show it for $3^x\cdot 5^y$? $\endgroup$ – David Diaz Oct 12 '19 at 21:02
  • 2
    $\begingroup$ How do you write $14$ for example? $\endgroup$ – user289143 Oct 12 '19 at 21:16
1
$\begingroup$

This is false. The number $14$ cannot be written this way.

Clearly $14$ is not of the form $2^a \cdot 3^b$, but it is also straightforward to check that there are no $a,b,c$ such that $14=3^a+2^b\cdot 3^c$, simply check $a,b,c\in\{0,1,2\}$ (numbers get too big outside this range).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.