20200228, 09:38  #1 
Mar 2018
2×269 Posts 
how to proof this fact
I want to proof that
if 23*34^x +5590*y+588 and 223*34^x+5590*y+588 are multiple of 43 for some positive x and y, then they are congruent to 344 mod 559 how to proof it? example: 23*34^2+5590*2+588 is multiple of 43 and so it is congruent to 344 mod 559 Last fiddled with by enzocreti on 20200228 at 09:43 
20200228, 11:28  #2 
Jun 2003
2^{2}·7·193 Posts 
559 = 13 * 43
If something is 344 (mod 559), it is the same as simultaneously being 6 (mod 13) and 0 (mod 43) ( read up on Chinese Reminder Theorem to understand this equivalence) Periodicity of 34^x (mod 13) is 4, and (mod 43) is 42. Wait! 4 doesn't divide 42. Doesn't look like your observation is true. Try 23*34^44 +5590*y+588. This is 0 (mod 559). Disproved! 
20200228, 11:38  #3  
Mar 2018
2·269 Posts 
...
Quote:
Ok so it is congruent to either 0 or 344 mod 559 

20200228, 15:48  #4  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×3,313 Posts 
your "proofs" are all built on "Tigger's principle".
"This!" Disproven. "Ok then this or that" Disproven. "Ok then this or that or that" and so on Quote:


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