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Old 2020-03-02, 14:55   #1
enzocreti
 
Mar 2018

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Default Numbers congruent to + or - (10^m*2^n) mod 216

If N is even consider

N is congruent to (10^m*2^n) mod 216 with(10^m*2^n)<216 for some nonnegative m, n


IF N is odd CONSIDER N is congruent to - (10^m*2^n) mod 216 with(10^m*2^n)<216 for some nonnegative m and n

Which N's satisfy one of the above modular equations?

AND WHAT if we add the restriction that (10^m*2^n) must be congruent to 2^k<(10^m*2^n) mod 13 for some k?

I ask this because possibly it is related to exponents of pg primes congruent to 0 mod 43

215 696660 92020 and 541456 infact are congruent to + or - (2^m*10^n) mod 216

Last fiddled with by enzocreti on 2020-03-02 at 15:33
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Old 2020-03-03, 06:12   #2
carpetpool
 
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"Sam"
Nov 2016

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Quote:
Originally Posted by enzocreti View Post
If N is even consider

N is congruent to (10^m*2^n) mod 216 with(10^m*2^n)<216 for some nonnegative m, n


IF N is odd CONSIDER N is congruent to - (10^m*2^n) mod 216 with(10^m*2^n)<216 for some nonnegative m and n
IF N is odd, it can NEVER be congruent to - (10^m*2^n) mod 216 (unless m and n are both zero), so I don't see the point to go any futher.
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