Is there a real number r such that

Wronsonia8g

Wronsonia8g

Answered question

2022-07-04

Is there a real number r such that all r n are irrational for all integers n 1 but it is not transcendental?

Answer & Explanation

behk0

behk0

Beginner2022-07-05Added 14 answers

Yes: 1 + 2 , for instance.
( 1 + 2 ) n = 1 + 2 ( n 2 ) + 2 2 ( n 4 ) + + ( ( n 1 ) + 2 ( n 3 ) + 2 2 ( n 5 ) + ) 2 .
pipantasi4

pipantasi4

Beginner2022-07-06Added 6 answers

A number is transcendental if it is not root of any polynomial having coefficients in Q . A number such that r n is irrational n is only not a root of x n q, n q Q , but it could be not transcendental anyway, by being root of a polynomial coprime with the last one.

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