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This is not an answer but an observation. Let $n$ be an integer and $H(n)$ its Hamming weight. $H(n) <= 1+ \max( { H(d) |\ d\ {\rm divisor\ of\ } n-1 })$ in particular for $p$ a prime greater than 2 $H(p) <= 1+ \max( { H(d) |\ d\ {\rm proper\ divisor\ of }\ p-1 })$ It could suggest ways to attack this and related questions. |
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This is not an answer but an observation. Let $n$ be an integer and $H(n)$ its Hamming weight. $H(n) <= 1+ \max( { H(d) | d divisor of n-1 })$ in particular for $p$ a prime greater than 2 $H(p) <= 1+ \max( { H(d) | d proper divisor of p-1 })$ It could suggest ways to attack this and related questions. |
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