Given that the Euler's phi-function, $\phi(n)$ is always even for $n>1$,
I understand that $\phi(n)$ is never odd other than $1$.
I wish to know for what $k\in\mathbb{N}$ does the equation $\phi(n)=2k$ has no solution?
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1If $m$ is an odd number such that $2m+1$ is not prime, then there is no solution to $\phi(n)=2m,$ for just the simplest even example. – Thomas Andrews Dec 22 '21 at 17:51
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@ThomasAndrews, Can you kindly supply proof, a link will do too? Thanks for responding. – F. A. Mala Dec 23 '21 at 12:57