2019-08-23, 20:49 | #1 |
Mar 2016
2·5·41 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
5×353 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
2×5×599 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. |
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