[math-fun] mersenne primes and their multiples
I was wondering what primes can occur as factors of “sparse” integers, i.e. those with only a few 1s in their binary expansion. Contrapositively speaking, you might enjoy proving the following: any multiple of the Mersenne prime 2^k-1 has at least k 1s. - Cris
I like this puzzle a lot! Haven’t solved it yet… Jim Propp On Wednesday, September 12, 2018, Cris Moore <moore@santafe.edu> wrote:
I was wondering what primes can occur as factors of “sparse” integers, i.e. those with only a few 1s in their binary expansion.
Contrapositively speaking, you might enjoy proving the following: any multiple of the Mersenne prime 2^k-1 has at least k 1s.
- Cris
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Forgot to mention that I solved it. Cute. Jim On Wed, Sep 12, 2018 at 9:24 PM, James Propp <jamespropp@gmail.com> wrote:
I like this puzzle a lot! Haven’t solved it yet…
Jim Propp
On Wednesday, September 12, 2018, Cris Moore <moore@santafe.edu> wrote:
I was wondering what primes can occur as factors of “sparse” integers, i.e. those with only a few 1s in their binary expansion.
Contrapositively speaking, you might enjoy proving the following: any multiple of the Mersenne prime 2^k-1 has at least k 1s.
- Cris
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Cris Moore -
James Propp