mersenneforum.org euler phi function and quadratic irred. polynomials
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 2019-08-23, 20:49 #1 bhelmes     Mar 2016 397 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 Nick     Dec 2012 The Netherlands 175910 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 Dr Sardonicus     Feb 2017 Nowhere 577710 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.

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