$n$ is an odd positive integer such that $\varphi(n)$ and $\varphi(n+1)$ are both powers of two . Here , $\varphi(n)$ denotes Euler's totient function. 

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> Is it true that $(n+1)$ is either $6$ or a power of $2$? 
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Please help me to prove or disprove this statement . (I was randomly flipping through some values attained by the $\varphi$ function when I observed this pattern) :)