Find an irrational n such that

seupeljewj

seupeljewj

Answered question

2022-06-27

Find an irrational n such that n n is a rational number.

Answer & Explanation

Trey Ross

Trey Ross

Beginner2022-06-28Added 30 answers

Let n be such that
n n = 2 ,
and let n be the irreducible fraction r s .
Then
( r s ) r / s = 2
or
r r = 2 s s r .
So r is even and s odd, and calling ρ the multiplicity of the factor 2 in r,
r ρ = s
and r = 1, a contradiction.
As a corollary, ln 2 W ( ln 2 ) is indeed irrational.

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