Does m necessarily be of the form 215s+129?

[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?

[carpetpool]

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.