Timeline for Integral polynomials dividing N!
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2016 at 18:43 | comment | added | Greg Martin | I agree. To elaborate briefly on "essentially equivalent": once $P(n)$ is $x$-friable, the only other test to pass is that the power of $p$ dividing $P(n)$ is at most the power of $p$ dividing $n!$, for all primes $p$. It's easy to show that most numbers are almost squareefree—say, only $O(x/\log x)$ numbers up to $x$ have a square factor larger than $\log x$—and that only $O(x/\log x)$ numbers up to $x$ are divisible by $p^r$ where $p<\log x$ and $p^r > \log^2x$. One has to adapt this to the set of values of a fixed polynomial, which requires some bookkeeping, but the principles are the same. | |
| Nov 12, 2016 at 1:30 | vote | accept | S. Pek | ||
| Nov 11, 2016 at 21:15 | history | answered | Lucia | CC BY-SA 3.0 |