20180309, 04:05  #12 
"Sam"
Nov 2016
2·163 Posts 
This can be done with basic algebra and modular math.
To get a set of basic solutions (m, D) write out: 29*5^m11 = 0 (mod 13) 29*5^m = 11 (mod 13) 5^m = 8 (mod 13) m = 3 (mod 4). So for any integer n, m = 3*n+4, D = (29*5^(3*n+4)11)/13 will be a solution to 29(5^m)11 = 13*D as you put it. 
20180309, 05:00  #13 
Aug 2006
5985_{10} Posts 
The solutions are M = 4k + 3, D = (3625*625^k  11)/13.
If b and n are relatively prime, you can find the general solutions to k(b^m)  z = nd by finding the order of b mod n, computing k(b^m)  z for m from 1 to the order, and taking any values which result in 0; these values, plus an arbitrary variable k times the order, are the possible values of m (and the d values can be computed from them). The case where b and n have a common divisor is not essentially different; you check the small cases, where some p  b and p^e  n, but p^e does not divide b, individually, then look at the order of b with all the common primes divided out mod n with all the common primes divided out. In the first case you could have 0 solutions or infinitely many; in the second case you could have finitely many or infinitely many. Edit: see carpetpool's post above. Last fiddled with by CRGreathouse on 20180309 at 05:01 
20180309, 05:43  #14 
Jun 2003
4,919 Posts 
OP sounds suspiciously like they're trying to sieve k*b^n+c form (variable n), in which case, just use newpgen or srsieve

20180309, 09:12  #15 
Feb 2018
2^{5}×3 Posts 
Are the cumulative product of (B^g).
Last step not. 
20180309, 09:20  #16 
Feb 2018
2^{5}·3 Posts 
Are the cumulative product of (B^g).
Starting with 1. And not the last step. Thats gives "bits one of D"="number steps". Rules are related to tserie used. Mersenne is tserie "n+e = (2^g)(e')". Most general: n+e=(B^g)(e') Any tserie as a equation. For Mersenne, (eLast)(B^M)(eStart)=n*D. Collatz is also a tserie. 1+3e=(2^g)(e'). But there are others tserie. Thanks for your interest. JMM 
20180309, 13:50  #17  
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 
Quote:


20180309, 15:29  #18 
"Sam"
Nov 2016
146_{16} Posts 

20180309, 15:32  #19 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 

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