mersenneforum.org Does m necessarily be of the form 215s+129?
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 2020-02-29, 17:59 #1 enzocreti   Mar 2018 21416 Posts Does m necessarily be of the form 215s+129? Let be N an integer congruent to 344 mod 559. Let be N either of the form 1763s+215 or 1763s+344. Now consider N is congruent to m mod (41*43*13). Does m necessarily be a number of the form 215k+129?
2020-03-01, 02:02   #2
carpetpool

"Sam"
Nov 2016

1010011002 Posts

Quote:
 Originally Posted by enzocreti Let be N an integer congruent to 344 mod 559. Let be N either of the form 1763s+215 or 1763s+344. Now consider N is congruent to m mod (41*43*13). Does m necessarily be a number of the form 215k+129?
Ahhh, simple modular arithmetic:

N = {344 mod 559, 215 mod 1763} = 14319 mod 22919
N = {344 mod 559, 344 mod 1763} = 344 mod 22919

Now,

344 = 129 mod 215
14319 = 129 mod 215

So the answer to your question is yes. You should be able to do the computations yourself without any struggle they are quite easy.

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