2019-08-23, 20:49 | #1 |
Mar 2016
101000010_{2} Posts |
euler phi function and quadratic irred. polynomials
A peaceful night for everyone,
Is it possible to calculate the euler phi function for the function terms of a quadratic irreducible polynomial like f(n)=n²+1 (n element of N) ? Or is there a hidden pattern ? Greetings from the tan (2 alpha) https://en.wikipedia.org/wiki/List_o...angle_formulae Bernhard |
2019-08-24, 08:26 | #2 |
Dec 2012
The Netherlands
11·151 Posts |
Calculating ϕ(n) is hard in the same sense that factorizing n is hard.
There may be patterns for some specific polynomials but I don't think you will find one in general. |
2019-08-24, 15:00 | #3 |
Feb 2017
Nowhere
11^{2}×37 Posts |
Here's a pattern:
If n is odd, then ϕ(n^{2} + 1) = ϕ((n^{2} + 1)/2) If n is even, then ϕ(n^{2} + 1) is divisible by 4. |
Thread Tools | |
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
primesieves for quadratic polynomials | bhelmes | Math | 21 | 2020-03-19 22:14 |
the multiplicativ structur of the discriminant for quadratic polynomials | bhelmes | Computer Science & Computational Number Theory | 3 | 2017-05-27 01:33 |
Basic Number Theory 7: idempotents and Euler's function | Nick | Number Theory Discussion Group | 17 | 2016-12-01 14:27 |
euler's totient function | toilet | Math | 1 | 2007-04-29 13:49 |
application of euler's phi function | TalX | Math | 3 | 2007-04-27 11:50 |