Find all odd numbers $n$ such that
$$ q= \dfrac{\ln(3n+1)}{6\ln(2)}$$ is also an odd number.
Asked
Active
Viewed 50 times
1 Answers
3
The equation is equivalent to: $$q=\log_{64}(3n+1)$$ or $$n=\frac{64^q-1}3$$
Since $64\equiv 1\pmod 3$, $n$ is an integer. And since $64^q-1$ is odd, $n$ is odd. So you only have to substitute $q$ for odd numbers, and you get the possible values of $n$.
ajotatxe
- 65,084
-
1Your statement "since $64^q−1$ is odd, $n$ is odd" is not true in itself, since an odd number divided by another odd number may be even. – Rory Daulton Oct 26 '14 at 12:47
-
2No, it cant be even. – Redundant Aunt Oct 26 '14 at 13:11
-
If you divide a number that has not the factor $2$ (that is, an odd number), the factor $2$ can't appear from the thin air in the quotient. – ajotatxe Oct 30 '14 at 15:43