Is there a real number r such that

Wronsonia8g 2022-07-04 Answered
Is there a real number r such that all r n are irrational for all integers n 1 but it is not transcendental?
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Answers (2)

behk0
Answered 2022-07-05 Author has 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 .

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pipantasi4
Answered 2022-07-06 Author has 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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