mersenneforum.org Numbers congruent to + or - (10^m*2^n) mod 216
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 2020-03-02, 14:55 #1 enzocreti   Mar 2018 10000011102 Posts 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
2020-03-03, 06:12   #2
carpetpool

"Sam"
Nov 2016

311 Posts

Quote:
 Originally Posted by enzocreti 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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