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

[QUOTE=enzocreti;538731]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
[/QUOTE]

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.