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Results tagged with probabilistic-number-theory
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user 37555
7
votes
Accepted
How many integers divide a number that involves just three non-zero digits?
For an integer $n$, call a prime divisor $p$ good, if the multiplicative order of $2$ modulo $p$ exceeds $p^{2/5}$, $p^2\nmid n$, and $(p-1, \varphi(n/p))<p^{1/5}$.
If $p$ is a good prime divisor of $ …
1
vote
Occurrence of simultaneous small remainders?
This is not always true. Suppose that $c_1+c_2=c_0$. Then $pc_1+pc_2\equiv pc_0\pmod{n}$. Hence if $pc_1\bmod n$, $pc_2\bmod n$ are in $[0, n^r]$, then $pc_0\bmod n$ is in $[0, 2n^r]$, which falls out …