Go Back > Math Stuff > Computer Science & Computational Number Theory

Thread Tools
Old 2019-08-23, 20:49   #1
bhelmes's Avatar
Mar 2016

1010000102 Posts
Default 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)

bhelmes is offline   Reply With Quote
Old 2019-08-24, 08:26   #2
Nick's Avatar
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.
Nick is offline   Reply With Quote
Old 2019-08-24, 15:00   #3
Dr Sardonicus
Dr Sardonicus's Avatar
Feb 2017

112×37 Posts

Here's a pattern:

If n is odd, then ϕ(n2 + 1) = ϕ((n2 + 1)/2)

If n is even, then ϕ(n2 + 1) is divisible by 4.
Dr Sardonicus is offline   Reply With Quote

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

All times are UTC. The time now is 20:33.

Tue Apr 20 20:33:48 UTC 2021 up 12 days, 15:14, 1 user, load averages: 3.63, 3.59, 3.49

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.