
Re: Looking for who originally conjectured the following theorem
Posted:
May 23, 2009 3:49 PM


Rainer Rosenthal wrote: > alainverghote@gmail.com schrieb: > > On 23 mai, 10:37, Rainer Rosenthal <r.rosent...@web.de> wrote: > >> alainvergh...@gmail.com schrieb: > >> > >>> but I found interesting to build a method for cases, > >>> Example: n = 71 , 2^p , p? > >> p=149, 2^p=713623846352979940529142984724747568191373312. > >> > >> Here is another easy one: n = 2, 71^p, p? > >> > >> Solution: p=4, 71^p=25411681. > >> > >> Cheers, > >> RR > > > > Bonjour Rainer, > > > > Well, why writing "easy one" if you do not mind > > explaining your way ? >I am going to post this under the natural number thread. My methods will be explained and out of the Einstein box far more interestring than standard stock Maple. Cheers, MMM(¤¤¤) I'll hit you with a link. Thank you. > Sorry, but it's not an especially interesting method. > Just checking ranges [n*10^m .. (n+1)*10^m1] whether or > not there is some b^k within this range, b being the base > in question. > The "easy" adjective is referring to the low exponent k, > resulting in a very short run of the search program (Maple): > > WhichPowerB := proc(n,b) # k: leadDig(b^k) = allDig(n) > local m,erg,k; > erg := 0; > for m from 0 to infinity do > k := floor(evalf(log[b](n*10^m))); > if n*10^m <= b^k and > b^k <= (n+1)*10^m1 then > erg := k; > break; > elif n*10^m <= b^(k+1) and > b^(k+1) < (n+1)*10^m1 then > erg := k+1; > break; > fi; > od: > print(n,erg,b^erg); > return; > end: > > For n = 1, 2, ... up to 10 we get: > > for n to 10 do > WhichPowerB(n,2); > od; > > n k 2^k >  > 1 0 1 > 2 1 2 > 3 5 32 > 4 2 4 > 5 9 512 > 6 6 64 > 7 46 70368744177664 > 8 13 8192 > 9 53 9007199254740992 > 10 10 1024 > > For your question regarding n=71: > > WhichPowerB(71,2); > 71, 149, 713623846352979940529142984724747568191373312 > > The "easy" one with base 71: > > WhichPowerB(2,71); > 2, 4, 25411681 > > (For n=2 and base b=10 one gets into trouble :) ) > > Best regards, > Rainer Rosenthal > r.rosenthal@web.de

