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 2020-02-28, 09:38 #1 enzocreti   Mar 2018 22·7·19 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 2020-02-28 at 09:43
 2020-02-28, 11:28 #2 axn     Jun 2003 19·283 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!
2020-02-28, 11:38   #3
enzocreti

Mar 2018

22·7·19 Posts
...

Quote:
 Originally Posted by axn 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!

Ok

so it is congruent to either 0 or 344 mod 559

2020-02-28, 15:48   #4
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3·19·173 Posts

Quote:
 Originally Posted by enzocreti Ok so it is congruent to either 0 or 344 mod 559
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:
 Originally Posted by https://en.wikipedia.org/wiki/Tigger#In_literature Most of the rest of that chapter is taken up with the characters' search for a food that Tigger can eat for breakfast — despite Tigger's claims to like "everything", it is quickly proven he does not like honey, acorns, thistles, or most of the contents of Kanga's larder.

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