Problem 652

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_epistemologist
Posts: 2
Joined: Mon Aug 13, 2018 12:58 am

Problem 652

Post by _epistemologist »

In the problem statement, it says
Note: According to the four exponentials conjecture the function logm(n) is proto-logarithmic. While this conjecture is yet unproven in general, log_m(n) can be used to calculate D(N) for small values of N.
Can we assume this conjecture for the given N=10^18?
brob26
Posts: 10
Joined: Thu Nov 22, 2018 3:48 am

Re: Problem 652

Post by brob26 »

_epistemologist wrote: Sun Jan 20, 2019 4:26 am Can we assume this conjecture for the given N=10^18?
If making this assumption leads you to a different answer, then you've disproved the four exponentials conjecture!

So either it's fine to assume the conjecture holds for larger N, or you settle a currently unsolved problem in number theory. Either way, progress is made :D
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