Help Me! My brain hurts.

[royanee]

Umm, I know I'm wrong, because there's no way I could be right. I just want to know how I'm wrong. Ok. I looked at the Proof of 78557 as a Sierpinski number. So I tried to do the same thing to 22699, because it was said to have a small number of holes. The problem is that my cycle length is 360 (0 to 359) and I think I covered it all. Here's my numbers:

Case A n 1 (mod 2) 22699.2n+1 is a multiple of 3
Case B n 0 (mod 4) 22699.2n+1 is a multiple of 5
Case C n 2 (mod 3) 22699.2n+1 is a multiple of 7
Case D n 6 (mod 12) 22699.2n+1 is a multiple of 13
Case E n 4 (mod 18) 22699.2n+1 is a multiple of 19
Case F n 10 (mod 18) 22699.2n+1 is a multiple of 57
Case G n 7 (mod 9) 22699.2n+1 is a multiple of 73

Thanks for the help.

[royanee]

Actually, just realized that I could make my cycle length 36, and drop the coverings of a few (so that all coverings are unique) to:

Case C n 2 (mod 12) 22699.2n+1 is a multiple of 7
Case E n 22 (mod 36) 22699.2n+1 is a multiple of 19
Case F n 10 (mod 36) 22699.2n+1 is a multiple of 57
Case G n 34 (mod 36) 22699.2n+1 is a multiple of 73

So for 0-35:
Odd n is covered by A.
Multiples of 4 are covered by B.
2 - C
6 - D
10 - F
14 - C
18 - D
22 - E
26 - C
30 - D
34 - G

[Jwb52z]

I wish there were a way to explain math better in words for those of us who don't understand the terms such as "mod".

[royanee]

Link:
http://www.teamprimerib.com/sob/78557.php

There are links on that page that explain everything they use. And there are links on those pages, ad infinitum... or so. I think I actually found my problem. I'm starting to believe that F isn't true and that my calculator is lying (rounding).

[rosebud]

Yeah, I think you're right. F isn't true, which is consistent with all remaining n's for 22699 being \equiv 10 (mod 36).

Sorry.

[royanee]

Thanks for replying! It was actually a lot of fun and taught me a lot about the process. :)

[jesterrace]

I gave it a try too and found out that all n \equiv 10 (mod 72) are multiples of 17....case 46 mod 72 seems hard tho :notworthy
Fun to try anyway :cheers: