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Old 2019-08-23, 20:49   #1
bhelmes
 
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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 ?


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Old 2019-08-24, 08:26   #2
Nick
 
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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.
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Old 2019-08-24, 15:00   #3
Dr Sardonicus
 
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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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