how to proof this fact

[enzocreti]

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

[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!

[enzocreti]

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

[Batalov]

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

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.