For which real number x is tan^3(x) + cot^3(x) a prime number?

 
 

Take all real numbers   x   for which    \tan \, x \; + \; \cot \, x    is a positive integer.
 

Find those of them for which    \tan^3 \, x \; + \; \cot^3 \, x    is a prime number.

 
 
 
Note that

 
TAN COT 1

TAN COT 2

TAN COT 3

 

Any other solutions?
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Prime Numbers and tagged , . Bookmark the permalink.

2 Responses to For which real number x is tan^3(x) + cot^3(x) a prime number?

  1. mcdonewt says:

    X +1/x #n. Prime.
    #1st solution 1+1 #2.
    Tan 45 deg #1.
    Other solution eg surds or continued fraction.
    x sq – nx +1#0.
    X= ( n +- sqrt (nsq -4))/2 …?
    Nsq # 4, 9, 25,49, 121, 169, 289, 361..

    query every prime n has a solution for
    Tan cub +cot cub #n.

    i haven’t tried these problems. Don newt

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