What is (x−1)/(x^(q/p)−1) equal to?

Maverick Avery

Maverick Avery

Answered question

2022-10-21

What is x 1 x q / p 1 equal to?

Answer & Explanation

dwubiegrw

dwubiegrw

Beginner2022-10-22Added 13 answers

Is there a polynomial P ( x ) (of finite degree, in C [ x ]) such that
( x 1 ) = ( x q / p 1 ) P ( x r )
for some rational r?
The answer is NO.
set x = z p and we get
( z p 1 ) = ( z q 1 ) P ( z r p )
Choose a (complex z) such that z q = 1 and z p 1
This is possible if ( p , q ) = 1 and q 1

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