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Old 2020-02-28, 11:28   #2
axn
 
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Jun 2003

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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!
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