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Results tagged with digits
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user 766
25
votes
Accepted
Total digit sum in distinct bases grow unboundedlly
As observed in comments, it suffices to show that for fixed $m,k$, there are only finitely many solutions in non-negative integers to the equation
$$ a^{x_1} + \dots + a^{x_m} = b^{y_1} + \dots + b^{y …
- 114k
25
votes
Accepted
The parity of the maximal number of consecutive 1s in the binary expansion of an integer
Perhaps surprisingly, the random variable $\ell(n)$ (with $n$ drawn uniformly from $[0,N)$) concentrates too much around $\log_2\log_2 N$ (where $\log_2$ denotes the logarithm to base $2$) to have a l …
- 114k