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Old 2022-09-14, 18:21   #1
enzocreti
 
Mar 2018

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Default How to prove that only Powers of 6^(6+35j) are of the form648+23004s

This Is a Little more difficult:

How to prove that Powers 6^(6+35j) for j nonnegative integer are of the form 648+23004s and only that powers .

I mean there Is no orher 6^g of the form 648+23004s, only Powers 6^(6+35j)

Last fiddled with by enzocreti on 2022-09-14 at 19:20
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Old 2022-09-15, 13:49   #2
Dr Sardonicus
 
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If a congruence holds (mod n), it holds (mod d) for every divisor d of n. In particular, in the case at hand, as you more or less pointed out in this post,

if 6^e == 648 (mod 23004), then

6^e == 648 (mod 71), or

6^e == 9 (mod 71).

Since 71 is a prime, the values of e are easily characterized.
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