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

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!

...
 

[QUOTE=axn;538499]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![/QUOTE]




Ok


so it is congruent to either 0 or 344 mod 559

[QUOTE=enzocreti;538500]Ok


so it is congruent to either 0 or 344 mod 559[/QUOTE]

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="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.
[/QUOTE]